Igor Ya. Subbotin, PhD

Math  isubboti@nu.edu         

 

Dr. Igor Ya. Subbotin

Professor

College of Letters and Sciences

Mathematics and Natural Sciences

Los Angeles Campus

isubboti@nu.edu

(310) 662-2150

 

 

Education

 

Ph.D. Mathematics,
Mathematics Institute of National Academy of Sciences of Ukraine, 1978

 

MS Mathematics
Kiev National Pedagogical University, 1972

 

 

Courses Taught

Algebraic Structures (MTH 416)

Linear Algebra (MTH 435)

Fundamentals of Mathematics I (MTH 209A)

Fundamentals of Mathematics II (MTH 301)

Topics in Modern Algebra (MTH 610, graduate)

Numbers Systems (MTH 620, graduate)

 

Research Interests

My main area of research is algebra. I investigate infinite and finite groups defined by prescribed properties of important families of subgroups and quotient groups, generalized normal subgroups and their influence on the structure of a group, infinite dimensional linear group, modules over group rings, and others. My second research interest is mathematics education. In this area, my work mostly dedicated to theoretical base of some topics of high school and college mathematics curriculum.

I have had the privilege to collaborate with several world-class mathematicians from different countries, including professors L.Kurdachenko, M. Dixon, J. Otal, N. Kuzennyi, V. Kirichenko, P. Shymyatskii, N. Semko, A. Russo, G. Vinchenzi, L. Kazarin, Z. Duan, and others.

 

 

Selected Publications (peer-reviewed)

 

1.  I.Ya. Subbotin,

Finite groups in which each subgroup of the derived subgroup is normal,

Mat. Zametki 12 (1972) 739-746;

English translation: Math. Notes 12 (1972) 882-885.

 

2.  I.Ya. Subbotin,

Finite p-groups in which every subgroup of the derived subgroup is normal,

Dopovidi Akademii Nauk (Proceedings of Academy of Sciences) of Ukrainian SSR,

Ser A. 12 (1974) 1072-1074.

 

 

3.  I.Ya. Subbotin,

Infinite finitely generated groups in which each subgroup of the derived subgroup is normal,Ukr. Mat. Zh. 27 (1975) 406-411; English translation: Ukr. Math. J. 27 (1975) 330-333.

 

4. I.Ya. Subbotin,

Finite soluble groups with the invariator condition for normal subgroups,

Studies on Group Theory, Inst. of Math. of Acad. of Sci. of Ukr.SSR, Kiev, (1976) 139-161.

 

5. I.Ya. Subbotin,

Finite insolvable groups with a quasicentralizer condition for normal subgroups. Akad. Nauk Ukrain. SSR Inst. Math. Preprint No. 16 (1977), 31 pages.

 

6. I.Ya. Subbotin,

Finite insoluble groups with the invariator condition for normal subgroups,

Group-Theoretical Studies, Naykova Dumka, Kiev, (1978) 94-117.

 

7. I.Ya. Subbotin,

Finite insoluble groups with the invariator condition for normal subgroups,

Theoretical and Applied Questions of Differential Equations and Algebra,

Naukova Dumka, Kiev, (1978) 241-243.

 

8. I.Ya. Subbotin,

Torsion soluble I(N)-groups, Groups Defined by Properties of the System of Subgroups, Inst. of Math. of Acad. of Sci. of Ukr.SSR, Kiev, (1979) 106-126.

 

9. I.Ya. Subbotin,

On infinite groups in which each subgroup of the derived subgroup is normal,

Constructive Description of Groups with Properties Prescribed on their Subgroups,

Inst. of Math. of Acad. of Sci. of Ukr.SSR, Kiev, (1980) 92-107.

 

10. I.Ya. Subbotin, Groups with the invariator condition for normal subgroups. Akad. Nauk Ukrain. SSR Inst. Mat. Preprint 1981, no. 7, 35 pages.

 

11.  I.Ya. Subbotin,

Infinite KI-groups with the Chernikov torsion part of the derived subgroup,

Investigation of Groups with Given Properties of the System of Subgroups,

Inst. of Math. of Acad. of Sci. of Ukr.SSR, Kiev, (1981) 79-93.

 

12. I.Ya. Subbotin,

On groups with the invariator condition, Subgroups Characterization of Groups,

Inst. of Math. of Acad. of Sci. of Ukr.SSR, Kiev, (1982) 99-109.

 

13. I.Ya. Subbotin,

On hypercentral coradical of KI-groups, Ukr. Mat. Zh. 34 (1982) 650-654;

English translation: Ukr. Math. J. 34 (1982) 532-536.

 

14. I.Ya. Subbotin and L.A. Perova,

General Algebraic Structures, Student’s manual, Kiev Polytechnic Institute, Kiev, (1982). 52 pages

 

15. I.Ya. Subbotin,

On quasicentralizer extensions of groups, Groups and Systems of their Subgroups,

Inst. of Math. of Acad. of Sci. of Ukr.SSR, Kiev, (1983)  86-92.

 

16. I.Ya. Subbotin,

Insoluble torsion groups with the invariator condition for normal subgroups, Izv. Vyssh. Ucheb. Zaved., Mat. #9 (1983) 56-64; English translation: Sov. Math. 27 (1983) 63-73.

 

17. I.Ya. Subbotin,

The quasicentral product of groups, Inst. of Math. of Acad. of Sci. of Ukr.SSR, Kiev, (1984)  126-139.

 

18. I.Ya. Subbotin,

The structure of nonperiodic groups wth the invariator condition for normal subgroups, Izv. Vyssh. Ucheb. Zaved., Mat.  #11 (1984)  40-45; English translation: Sov. Math. 28 (1984) 49-55.

 

19. I.Ya. Subbotin,

Groups decomposable into a quasicentralizer product, Ukr. Mat. Zh. 37 (1985) 648-651; English translation: Ukr. Math. J. 37 (1985) 529-531.

 

20. I.Ya. Subbotin and N.F. Kuzennyi,

Groups with the invariator condition on nonabelian normal subgroups, Structure of Groups and Properties their Subgroups, Inst. of Math. of Acad. of Sci. of Ukr.SSR, Kiev, (1986)  101-107.

 

21. N.F. Kuzennyi and I.Ya. Subbotin,

Groups in which all subgroups are pronormal, Ukr. Mat. Zh. 39 (1987) 325-329; English translation: Ukr. Math. J. 39 (1987) 251-254.

 

22. I.Ya. Subbotin and N.F. Kuzennyi,

Soluble groups with the invariator condition on nonabelian normal subgroups,

Izv. Vyssh. Ucheb. Zaved., Mat.  #10 (1987)  68-70; English translation: Sov. Math. #10 (1987) 91-94.

 

23. V.I. Kost’uk, V.N. Kirichkov, and I.Ya. Subbotin,

Flexible Identification of Systems and Objects. Mathematical Models and Structural Identification, Kiev Polytechnic Institute, State Department of Higher Education, Kiev, (1987), 90 pages.

 

24. I.Ya. Subbotin and N.F. Kuzennyi,

On groups with a transitive condition, Studies of Groups with Restrictions on Subgroups, Inst. of Math. of Acad. of Sci. of Ukr.SSR, Kiev, (1988) 73-80.

 

25. N.F. Kuzennyi and I.Ya. Subbotin,

On non-splittable groups extensions, Studies of Groups with Restrictions on Subgroups, Inst. of Math. of Acad. of Sci. of Ukr.SSR, Kiev, (1988)  27-33.

 

26. N.F.Kuzennyi and I.Ya. Subbotin,

A new characterization of locally nilpotent `IH-groups, Ukr. Mat. Zh. 40 (1988) 322-326; English translation: Ukr. Math. J. 40 (1988) 274-277.

 

27. I.Ya. Subbotin and N.F. Kuzennyi,

Locally soluble groups in which all infinite subgroups are pronormal, Izv. Vyssh. Ucheb. Zaved., Mat.  #11(1988)  77-79; English translation: Sov. Math. #11 (1988)  126-131.

 

28. N.F. Kuzennyi and I.Ya. Subbotin,

Groups with pronormal primary subgroups, Ukr. Mat. Zh. 41 (1989) 323-327; English translation: Ukr. Math. J. 41 (1989)  286-289.

 

29. N.F. Kuzennyi and I.Ya. Subbotin,

Locally soluble groups with the transitive condition for infinite nonabelian normal subgroups, Methods of Investigations of Algebraic and Topologic Structures, Kiev State Pedagogic University, Kiev, (1989) 45-52.

 

30. I.Ya. Subbotin and N.F. Kuzennyi,

Groups all of which subgroups have a fan of a given type, Ukr. Mat. Zh. 42 (1990) 1232-1236; English translation: Ukr. Math. J. 42 (1990)  1096-1100.

 

31. N.F. Kuzennyi, I.Ya. Subbotin, and L. Tomanek,

On some extensions of quasicyclic groups, Collect. Sci. Works of Pedag. Department of Pressove University, Math., Kosice, XXIV (1990) 99-123.

 

32. I.Ya. Subbotin,

Weakly central extensions of groups, Ukr. Math. J. 43 (1991) 1017-1021; English translation: Ukr. Math. J. 43 (1991)  951-953.

 

33. I.Ya. Subbotin,

On ZD-coradical of a KI-group, Comp. & Appl. Math., Kiev University Press, 73 (1991) 120-124.

 

34. I.Ya. Subbotin,

Groups in which the derived subgroup is generated by cyclic invariant subgroups,

Comp. & Appl. Math., Kiev University Press, 74 (1992) 85-88; English translation:

J. Math. Sc., 1994, 72, # 2, 3038-3040.

 

35. I.Ya. Subbotin and N.F. Kuzennyi,

On groups with fan subgroups, Contemporary Mathematics 131 (1992) Part 1 383-388.

 

36. I.Ya. Subbotin,

Groups with alternatively normal subgroups, Izv. Vyssh. Ucheb. Zaved., Mat.  #3 (1992)  86-88; English translation: Sov. Math. #3 (1992) 87-89.

 

37. N.F. Kuzennyi, S.S. Levischenko, and I.Ya. Subbotin,

Some results on description of torsion T(A)-groups with an abelian locally nilpotent coradical, Third International Conference on Algebra, Proceedings, Krasnoyarsk (1993), 189-190.

 

38. I.Ya. Subbotin

Groups with pronormal subgroups of proper normal subgroups,

Proceeding of the international conference “Infinite Groups 1994”, Walter der Gruyter, Berlin, 1995, 247-256

 

39. L.A. Kurdachenko and I.Ya.Subbotin

Groups with restrictions for cocentralizers of elements. Communications in Algebra, 24, #3 (1996) 1173-1187.

 

40. L.A. Kurdachenko, B.I. Petrenko, I.Ya.Subbotin,

On generalized hypercenters in artinian modules, Communications in Algebra, 25(4) (1997) 1023-1046.

 

41. L.A. Kurdachenko, J. Otal, I.Ya. Subbotin

Just-non-X-groups and related modules. A survey and the newest results, Publ. Del Seminario Matematico Garcia De Galdeno (Serie II) University de Saragoza, section 1 #3 (1997) 1-30.

 

42. L.A. Kurdachenko, B.I. Petrenko, I.Ya.Subbotin,

On the complementation of some generalized hypercenters in artinian modules, Ukrainian Math. Journal, 49, # 11 (1997) 11-15.

 

43. L.A. Kurdachenko, B.I. Petrenko, I.Ya.Subbotin,

Direct decompositions in artinian modules over FC-hypercentral groups, Contemporania Matematika, 14 (1998) 89-100.

 

44. M. De Falco, L.A. Kurdachenko, I.Ya. Subbotin

Groups with only abnormal and subnormal subgroups, Atti del Seminario Matematico e Fisico dell’Universita di Modena, 2 (1998) XLVI 435-442.

 

45. L.S. Kazarin, L.A. Kurdachenko, I.Ya. Subbotin

Groups saturated with abelian subgroups, The International Journal of Algebra and Computation, 8 (1998) 443-466.

 

46. L.A. Kurdachenko and I.Ya Subbotin

Groups whose proper quotients are hypercentral, Journal of the Australian mathematical Society (Series A) 65 (1998), 224-237.

 

47. Z.Y. Duan, L.A. Kurdachenko, I.Ya. Subbotin

Artinian modules over hyperfinite groups Southeast Asian Bulletin of Mathematics, 2 (1998) 273-286.

 

48. L.A. Kurdachenko, J. Otal, I.Ya. Subbotin

Groups with Many Similar Factor-Groups, University of Zaragoza, Spain, 1998, 186 pages.

 

49. L.A. Kurdachenko, I. Ya. Subbotin

Groups with many periodic factor-groups, Communications in Algebra, 28(3), 2000, 1593-1602.

 

 

50. L.A. Kurdachenko, I. Ya. Subbotin

On artinian modules over hyperfinite groups.  Algebra and its Applications, AMS, Contemporary Mathematics, 259, 2000, 323-331.

 

51. L.A. Kurdachenko, I. Ya. Subbotin

On the quasicentralizer condition. Southeast Asian Bulletin of Mathematics, 24 (2000) 565-572

 

52. L.A. Kurdachenko, I. Ya. Subbotin

On some infinite dimensional linear groups. Communications in Algebra, 29(2), 519-527 (2001)

 

53. L.A. Kurdachenko, P. Shumyatsky, I. Ya. Subbotin

Groups with many nilpotent subgroups. Algebra Colloquium, 8(2) 129-143 (2001).

 

54. L.A. Kurdachenko, I. Ya. Subbotin

On minimal artinian modules and minimal artinian linear groups. International Journal of Mathematics and Mathematical Sciences 27(12), 704-714 (2001)

 

55. L.A. Kurdachenko, N.V. Polyakov, I. Ya. Subbotin

On some generalization of a theorem of B. H. Neumann. Matematica Contemporanea, 21 (2001), 131-145

 

56. L.A. Kurdachenko, J. Otal, I. Ya. Subbotin

Groups with bounded Chernikov conjugacy classes, Ukrain. Math. J. 54 (2002) no 6, 792-807

 

57. L.A. Kurdachenko, J. Otal, I. Ya. Subbotin

On some criteria of nilpotency, Commun. Algebra, 30 (2002) 8, 3755-3776

 

58. L.A. Kurdachenko, I. Ya. Subbotin

On transitivity of abnormality, Publicationes Mathematicae, Debrecen, 61 (2002) 3-4, 479-486

 

59. L.A. Kurdachenko, I. Ya. Subbotin

On transitivity of pronormality, Comment. Matemat. Univ. Caroline, 43 (2002) 4, 583-594

 

60. L.A. Kurdachenko, I. Ya. Subbotin

On some infinite dimensional linear groups II, Southeast Asian Bulletin of Mathematics, 26 (2002), 773-787

 

61. L.A. Kurdachenko, I. Ya. Subbotin

On U-normal subgroups, Southeast Asian Bulletin of Mathematics, 26 (2002), 789-801

 

62. L.A. Kurdachenko, N.V. Polyakov, I.Ya. Subbotin

On combinatorial characteristics of some infinite groups, Proceeding of National Academy of Sciences of Ukraine, 11 (2002), 17-19

 

63. L. A. Kurdachenko, J. Otal, I. Ya. Subbotin,

Baer-like decompositions of modules, Illinois Journal of Mathematics, v 47 (2003), issues 1-2, 329-343.

 

64. L. A. Kurdachenko, I. Ya. Subbotin,

Pronormality, contranormality and generalized nilpotency in infinite groups,

Publicacions Matematiques. 47 (2003), 389-414

 

65. L. A. Kurdachenko, I. Ya. Subbotin,

On some infinite dimensional linear groups. Groups St Andrews 2001 in Oxford, London Math. Soc. Lecture Note Series, Cambridge University Press, v.305 (2003), 377-384.

 

66. L.A. Kurdachenko and  I.Ya. Subbotin,

On some types of Noetherian modules, Journal of Algebra and Its Applications, Vol. 3, No. 2 (2004) 169-179.

 

67. L.A. Kurdachenko and  I.Ya. Subbotin,

Abnormal subgroups and Carter subgroups in some infinite groups, Algebra and Discrete Mathematics, Number 1. (2005). pp. 63 – 77.

 

68.L.A. Kurdachenko, N.N. Semko  and  I.Ya. Subbotin

Artinian modules over FC-hypercental groups.  Proceedings of the National Academy of Sciences of Ukraine Number 2 (2005), 29 - 32

 

69. N.F. Kuzennyi and I.Ya. Subbotin

On semiablelian groups. International Journal of Mathematics and Mathematical Sciences (IJMMS) 12 (2005), 1989-1994

 

70. L. A. Kurdachenko, J. Otal, I. Ya. Subbotin,

Abnormal, pronormal, contranormal, and Carter subgroups in some generalized minimax groups, Communications in Algebra, Volume 33, Number 12 (2005), 4595 – 4616.

 

71. L. A. Kurdachenko, I. Ya. Subbotin,

Linear groups with the maximal condition on subgroups of infinite central dimension, Publicacions Matemàtiques, Vol. 50, Number 1 (2006), 103-131.

 

72. L.A.Kurdachenko and I.Ya. Subbotin,

Transitivity of normality and pronormal subgroups. Contemporary Mathematics, American Mathematical Society, v. 421 (2006) p. 201-212.

 

73. L. A. Kurdachenko, J.Otal and I.Ya. Subbotin,

On properties of abnormal and pronormal subgroups in some infinite groups. Groups St. Andrews 2005. Cambridge University Press, Series: London Mathematical Society Lecture Note Series (No.340), 2007. p. 772-782.

 

74. L. A. Kurdachenko, N. N. Semko and I.Ya. Subbotin,

Artinian modules over FC-hypercentral groups, Journal of Algebra and Its Applications, Vol. 6, No. 3 (2007) 527-551.

 

75. L. A. Kurdachenko, I. YA. Subbotin, V. A. Chupordya,

On bounded artinian-finitary modules. International Journal of Algebra and Computation, Vol. 17, No. 4 (2007) 881-893.

 

76.  L. A. Kurdachenko, I. YA. Subbotin, V. A. Chupordya,

About bounded artinian finitary modules. Proceedings of the National Academy of Sciences of Ukraine Number 10 (2007), 23 – 26

 

77. L. A. Kurdachenko, I Ya. Subbotin,

On some soluble groups in which U-subgroups form a lattice. Comment.Math.Univ.Carolin. 48, No 4 (2007), 585-593.

 

78. L.A. Kurdachenko, N.F. Kyzennii, N.N. Semko, I.Ya. Subbotin,

On some questions of generalized soluble group theory. Bulletin of University of Kiev, Series: Physics & Mathematics, 3 (2007), 32-44.

 

 79. M. Dixon, L. Kurdachenko, Subbotin, I.

On various rank conditions in infinite groups. Algebra and Discrete Mathematics. 4 (2007), 23-43.

 

80. L.A. Kurdachenko, A. Russo, I.Ya. Subbotin, and G. Vincenzi,

Infinite groups with short balanced chains of subgroups. Journal of Algebra 319 (2008) issue 9, pp. 3901-3917.

 

81. L. A. Kurdachenko, A. V. Sadovnichenko and I.Ya. Subbotin.

On some infinite dimensional linear groups. Central European Journal of Mathematics, Volume 7, (2009) n. 2, 176-185

 

82. Kurdachenko, L., Subbotin, I., Chupordya, V.

On some close to nilpotent groups. Fundamental and Applied Mathematics. v. 14, (2009) n. 6, 121-134. English translation:

Journal of Mathematical Sciences, v. 164 (2010) Number 1, 82-90

 

83. L. A. Kurdachenko, J.Otal and I.Ya. Subbotin,

Criteria of nilpotency and influence of contranormal subgroups on the structure of infinite groups. Turk. J. Math., 33, (2009), 227-237.

 

84. V.V. Kirichenko, L.A. Kurdachenko, N.N. Semko, I.Ya. Subbotin,

Nikolai F. Kuzennyi: to his sixties birthday. Algebra Discrete Math. 2009, no. 1, E--H.

 

85. L.A. Kurdachenko, J. Otal, I.Ya. Subbotin,

On Influence of Contranormal Subgroups on the Structure of Infinite Groups. Communications in Algebra, Volume 37 (2009) Issue 12, 4542 – 4557

 

86. M. R. Dixon, I. Ya. Subbotin,

Groups with finiteness conditions on some

subgroup systems: a contemporary stage. Algebra and Discrete Mathematics, 4 (2009), 29-54

 

87. I. Ya. Subbotin,

On arrangement of subgroups in groups and related topics: some recent developments. Algebra and Discrete Mathematics, 4 (2009), 185 -207.

 

88. L. A. Kurdachenko, A. V. Sadovnichenko and I. Ya. Subbotin,

Infinite dimensional linear groups with many G - invariant subspaces, Central European Journal of mathematics, 8 (2010) n 2, 261-265

 

89.  L.A. Kurdachenko, I. Subbotin, V. Chupordya,

On groups whose proper subgroups are pronormal or subnormal. Proceedings of National Academy of Sciences of Ukraine (Dopovidi Nacional’noii Academii Nayuk of Ukraine), 1 (2010), 17-20

 

90. M.R. Dixon, L.A. Kurdachenko, I.Ya. Subbotin.

On the concepts of the rank ininfinite groups. On the Influence of Some Important Types of Subgroups on the Structure of a Group. A collection of survey articles. In-t Math of NAS of Ukraine, Kiev -2010, 59-113.

 

91. M.R. Dixon and I.Ya. Subbotin.

Groups with finiteness conditions on some subgroup systems: a contemporary stage. On the Influence of Some Important Types of Subgroups on the Structure of a Group. A collection of survey articles. In-t Math of NAS of Ukraine, Kiev -2010, 115-153.

 

92. V.V. Kirichenko, L.A. Kurdachenko and I.Ya. Subbotin.

On new developments in the investigation of groups with prescribed restrictions on some influential families of subgroups. On the Influence of Some Important Types of Subgroups on the Structure of a Group. A collection of survey articles. In-t Math of NAS of Ukraine, Kiev -2010, 155-206.

 

93. L. A. Kurdachenko, Alexsandr A. Pypka, Igor Ya. Subbotin,

On some properties of pronormal subgroups, Cent. Eur. J. Math. 8(5) (2010), 840-845

 

94. L. A. Kurdachenko, Javier Otal, Igor Ya. Subbotin,

Some criteria for existence of supplements to normal subgroups and their applications. International Journal of Algebra and Computation, Vol. 20, No. 5 (2010), 689–719

 

95. L. A. Kurdachenko, A. V. Sadovnichenko, I. Ya. Subbotin,

Infinite dimensional linear groups with a large family of G-invariant subspaces. Comment. Math. Univ. Carolin.  51,4 (2010) 551-558

 

96. L.A. Kurdachenko, O.O. Pypka, I.Ya. Subbotin,

A characterization of pronormal subgroups in some classes of infinite groups. (Ukrainian. English summary) Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2011, No. 1, 23-27 (2011).

 

97. L.A. Kurdachenko, J. Otal, I.Ya. Subbotin,

Pronormal subgroups and transitivity of some subgroup properties. Groups St Andrews 2009 in Bath: Volume 2, London Mathematical Society, 2 (2011), 448-460.

 

98. V. V. Kirichenko, L. A. Kurdachenko and I. Ya. Subbotin,

Some related to pronormality subgroup families and properties of the group. Algebra and Discrete Mathematics. Volume 11 (2011). Number 1. pp. 75 – 108.

 

99. L.A. Kurdachenko, I.Ya. Subbotin, T.I. Ermolkevich,

Groups whose finitely generated subgroups are either permutable or pronormal. Asian-European Journal of Mathematics, Vol. 4, No. 3 (2011), 459-473.

 

100. L.A. Kurdachenko, I.Ya. Subbotin,

On Groups whose contranormal subgroups are normally complemented. Serdica Math. J. 37 (2011), 163–172.

 

101. V. V. Kirichenko, L. A. Kurdachenko, J. Otal and I. Ya. Subbotin,

On the contribution of D.I. Zaitsev to the Theory of Infinite Groups, Algebra and Discrete Mathematics, 13 (2012). #1. 59 – 91

 

102. L. A. Kurdachenko, A. A. Pypka, I. Ya. Subbotin,

On some generalizationsof normal subgroups. Biblioteca de la Revista Matem´atica Iberoamericana, Proceedings “Encuentro en Teor´ıa de grupos y sus aplicaciones” (Zaragoza, 2011), 185–202.

 

103. M. R. Dixon,V. V. Kirichenko, L. A. Kurdachenko, J. Otal, N. N. Semko, L. A. Shemetkov,  I. Ya. Subbotin,

S. N. Chernikov and the development of infinite group theory. Algebra and Discrete Mathematics. Volume 13 (2012). Number 2. pp. 169 – 208.

 

104. Kurdachenko, L.A.; Pypka, O.O.; Subbotin, I.Ya.

On some connections and generalizations of pronormal subgroups. (Ukrainian. English summary). Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2012, No. 3, 24-27 (2012).

 

105. Kurdachenko, L.A.; Ermolkevich T.V.; Subbotin, I.Ya.

On the structure of periodic groups whose finitely generated subgroups are either permutable or pronormal. (Ukrainian. English summary). Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2012, No. 5, 23-25 (2012).

 

106. L. A. Kurdachenko, N. N. Semko (Jr.), I. Ya. Subbotin,

Groups with many pronormal and transitively normal subgroups. Algebra and Discrete Mathematics,

14 (2012), No 1. pp. 84-106

 

107. L. A. Kurdachenko, I. Ya. Subbotin, T. I. Ermolkevich,

On non-periodic groups whose finitely generated subgroups are either permutable or pronormal. Mathematica Bohemica, 138 (2013), No 1, 61-74.

 

108.  L. A. Kurdachenko, J. Otal, I. Ya. Subbotin,

On permutable fuzzy subgroups. Serdica Math. J., 39 (2013), 83–102

 

109. L. A. Kurdachenko, I. Ya. Subbotin,

The groups whose subgroups are almost ascendant. Asian-European Journal of Mathematics, Vol. 6, No. 1 (2013) 1350014 (8 pages)

 

 

Mathematics Education

 

1.  I.Ya. Subbotin, M.S. Yakir

To improve, not to reject. Mathematics in School, # 1, 1989, p.76-77

 

2.  V.N. Lyisenko, I.Ya. Subbotin, E.D. Agey, L.N. Kuznetcova, L.A. Spashiba

Practicum on geometry for students. Manual for students, Kiev Polytechnic Institute Press, Kiev 1988, 59 pages.

 

3. S.S. Levischenko, I.Ya. Subbotin, M.S. Yakir

Some elementary consequences of the Dirichlet Theorem. Mathematics World, Radyan’ska Schola, Kiev, # 19, 1989, p. 114-119.

 

4. I.Ya. Subbotin, M.S. Yakir

Aan educational function of a mistake. Mathematics in School, # 2-3, 1992, p.27-28.

 

5.  S.S. Levischenko, I.Ya. Subbotin, M.S. Yakir

Around of the Bertran Postulate.  Mathematics World, # 2, 1996, 56-61.

 

6.  N.N. Bilotckiy, I.Ya. Subbotin, L. Y. Khilchenko,

An algorithmic approach to the notion of elementary function.   Mathematics in School, # 2, 1998, 67-73.

 

7. N.N. Bilotckiy, I.Ya. Subbotin, L. Y. Khilchenko,

Mathematics education in American schools. Mathematics in School, # 3, 2000, 67-73.

 

8. P. Serduykov, I. Subbotin, N. Serdyukova,

Accessible, Convenient & Efficient education for working adults in a shorter time: Is It Possible?  CAEL Forum and News, Spring 2003, v. 26, issue 3. 24-28.

 

9. I. Subbotin, N. Serdyukova, &  P. Serdyukov.

Short-term Intensive College Instruction: What are the Benefits for Adult Learners?. In C. Crawford et al. (Eds.), Proceedings of Society for Information Technology and Teacher Education International Conference 2003 (pp. 1550-1552). Chesapeake, VA: AACE.

 

10. I. Subbotin, H. Badkoobehi, N. Bilotckiy:  Application of fuzzy logic to learning assessment. Didactics of Mathematics: Problems and Investigations. - Issue 22, 2004. - 136 p., pp. 38-41 (International program “Heuristics and didactics of the hard sciences”).

11.  N. Bilotskii, I. Subbotin, M. Hill.  Properties of function in one variable, determined by the group of rigid motions of the number line.   Didactics of Mathematics: Problems and Investigations. - Issue 23. 2005, p. 60-70.

12. I. Subbotin, H.  Badkoobehi, H., N. Bilotskii, Fuzzy logic and learning assessment. DIDACTICS  of  MATHEMATICS: Problems and Investigations.  Issue # 24 (2005) p. 112-118

13. I. Subbotin, N.  Bilotskii, M. Hill, Inter-topic connections as a way of realizing of inter-subject connections (the group of rigid motions of the number line and the properties of a real function in one variable). Mathematics in School, 9 (2005), p. 38-45

 

14. I. Subbotin, F.  Mossavar-Rahmani, N.  Bilotskii, N.N. Fuzzy logic and iterative assessment. DIDACTICS  of  MATHEMATICS: Problems and Investigations.  Issue # 25 (2006), p. 221-227.

 

15. I. Subbotin, N.  Bilotskii, M. Hill Mathematics teachers’ development in California (USA) and Ukraine:  Brief comparative analysis. Didactics of  Mathematics: Problems and Investigations.  Issue # 26 (2006), p 79-85.


16.  I. Subbotin, N.  Bilotskii, M. Hill, Mathematics teachers’ development in California (USA): California subject examinations for teachers. Didactics of  Mathematics: Problems and Investigations.  Issue # 27 (2007),  p 63 - 68.

 

17. I. Subbotin, N. Bilotskii, Algorithms and fundamental concepts of Calculus, Journal of Research in Innovative Teaching, 1 (2008), 10 pages.

 

18. N. Bilotskii, I. Subbotin, P. Baryshovetc.  On the definition of the directional derivative in Calculus courses. Didactics of Mathematics: Problems and Investigations.  Issue # 29 (2008), p. 57-64.

 

19. L. Kurdachenko, I. Subbotin. An Integrated Approach in Teaching Algebra and

Number Theory: Best Practices.  Didactics of Mathematics: Problems and Investigations.  Issue # 30 (2008), p. 89-93.

 

20. N.N. Bilotskii, I.Ya. Subbotin. Inter-subject connections in teaching of mathematics: isometries of a number line and some fundamental properties of functions. Journal of Research in Innovating Teaching. 2 (2009), p. 138-147

 

21. I.Subbotin , F.Mossovar-Rahmani , N.Bilotskii. Fuzzy logic and the concept of the zone of proximate development. Didactics of Mathematics: Problems and Investigations. –Doneck, 2011. v.36.  p.101–108.

 

22. I. Ya. Subbotin, M. Gr. Voskoglou, Applications of fuzzy logic to Case-Based Reasoning, International Journal of Applications of Fuzzy Sets (ISSN 2241-1240) Vol. 1 ( 2011), 7-18

 

23. M. Gr. Voskoglou, I. Ya. Subbotin, Fuzzy Models for Analogical Reasoning, International Journal of Applications of Fuzzy Sets (ISSN 2241-1240), Vol.2 (2012), 19-38.

 

24. І.Subbotin, N. Bilotskii, Fuzzy logic application to assessment of results of iterative learning. Didactics of Mathematics: Problems and Investigations, 2012. v.37. p.89-93.

 

 

Cybernetics

1.  V.N. Kirichkov, I.Ya. Subbotin, E.I. Zhukina

Isolation of linearly dependent vectors. Adapt. Systems of Automat. Control, # 14, 1986, p.31-36.

 

2.  V.I. Kost’uk, V.N. Kirichkov, I.Ya. Subbotin

Flexible identification of systems and objects.  Mathematical models and structural identification.  Vyischa shkola. Kiev, 1987, 90pp.

 

 

Books

 

M. R. Dixon, L.A. Kurdachenko, I. Ya. Subbotin. Algebra and Number Theory: an Integrated Approach. John Willey & Sons, Hoboken, New Jersey, 2011, 536 pages.

 

V.V. Kirichenko, L.A. Kurdachenko, N.N. Semko, I.Ya. Subbotin (editors), On the Influence of Some Important Types of Subgroups on the Structure of a Group. A collection of survey articles. Institute of Mathematics of National Academy of Sciences of Ukraine, Kyiv – 2010, 258 pages.

 

I.Ya. Subbotin, Guest Editor, Algebra and Discrete Mathematics, special issue # 4 (2009). Ukraine, Lugansk 2009, 209 pages.

 

L.A.Kurdachenko, N.N. Semko, I.Ya. Subbotin

Insight into Modules over Dedekind Domains, Institute of Mathematics of National Academy of Sciences, Series: Proceedings of Institute of Mathematics of NAS, v. 75, Kiev, 2008, 119 pages.

 

L. A. Kurdachenko, J. Otal, I. Ya. Subbotin

Artinian Modules over Group Rings, Series: Frontiers in Mathematics, Birkhauser: Basel, 2007, XII, 247 pages.

 

L.A. Kurdachenko, J. Otal, I. Ya. Subbotin

Groups With Prescribed Quotient Groups and Associated Module Theory,

World Scientific: New Jersey, London, Singapore, Hong Kong, 2002, XII, 255 pages.

 

L.A. Kurdachenko, J. Otal, I.Ya. Subbotin

Groups with Many Similar Factor-Groups, University of Zaragoza, Spain, 1998, 186 pages.

 

V.I. Kost’uk, V.N. Kirichkov, I.Ya. Subbotin

Flexible Identification of Systems and Objects:  Mathematical Models and Structural Identification.  Vyischa Shkola. Kiev, 1987, 90 pages.