Kazarin, Lev Sergeevich

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Total publications: 38
Scientific articles: 35

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Doctor of physico-mathematical sciences (1986)
Speciality: 01.01.06 (Mathematical logic, algebra, and number theory)
Birth date: 27.08.1946
Keywords: algebra, group theory and generalizations, coding theory, finite algebras, signal theory, cryptography, mathematical education.


The problem of the non-simplicity of a finite group that is a product of two its permutable subgroups with non-trivial centers was solved. It was described the structure of the composition factors of a finite group which is a product of two its soluble subgroups. A number of papers devoted to the structure of a finite group which is a product of its permutable subgroups with given properties. In particular it was proved that the group $G$ which has a conjugacy class with prime power cardinality has a non-trivial soluble normal subgroup. The structure of the adjoint group of a finite nilpotent algebra was investigated together with B. Amberg. Arithmetical conditions on the degrees of irreducible representations of finite groups where investigated in some papers with Ya. G. Berkovich and I. M. Isaacs.


Graduated from Faculty of Mathematics and Mechanics of A. M. Gorkii (the chair of High Algebra and Geometry), the scientific adviser was professor P. I. Trofimov. Ph. D. thesis was defended in 1972. D. Sci. thesis was defended in 1986. A list of my works contains more than 100 titles.

The real member of the Russian Academy of Natural Sciences since 1997. In 2000 I was awarded the Peter the Great medal of the International Academy Sciences of Natural and Society for the papers on groups with factorizations.

Main publications:
  1. Kazarin L.S., “Priznaki neprostoty faktorizuemykh grupp”, Izv. AN SSSR, ser. matem., 44:2 (1980), 288–308  mathnet  mathscinet  zmath
  2. Kazarin L.S., “Soluble products of groups”, Infinite groups 1994, Proc. of the Internat. Conf. (Ravello, Italy, May 23–27, 1994), de Gruyter, Berlin, 1996, 111–123  mathscinet  zmath
  3. Kazarin L.S., “On groups which are the products of two solwable subgroups”, Comm. Algebra, 14:6 (1986), 1001–1066  crossref  mathscinet  zmath
  4. Kazarin L.S., “O $p^\alpha$-lemme Bernsaida”, Matem. zametki, 48:2 (1990), 45–48  mathnet  mathscinet  zmath
  5. Kazarin L.S., “O gruppakh, predlozhennykh Sidelnikovym”, Matem. sb., 189:7 (1998), 131–144  mathnet  mathscinet  zmath
  6. Zagorin D.L., Kazarin L.S., “Abelevy ABA-faktorizatsii konechnykh grupp”, Dokl. RAN, 347:5 (1996), 590–592  mathnet  mathscinet  zmath
List of publications on Google Scholar
List of publications on ZentralBlatt

Publications in Math-Net.Ru
1. L. S. Kazarin, S. S. Poiseeva, “On finite groups with an irreducible character large degree”, Model. Anal. Inform. Sist., 22:4 (2015),  483–499  mathnet  mathscinet  elib
2. L. S. Kazarin, I. A. Rassadin, D. N. Sakharov, “The existence of triple factorizations for sporadic groups of rank 3”, Model. Anal. Inform. Sist., 22:2 (2015),  219–237  mathnet  mathscinet  elib
3. L. S. Kazarin, S. S. Poiseeva, “Finite Groups with Large Irreducible Character”, Mat. Zametki, 98:2 (2015),  237–246  mathnet  mathscinet  elib; Math. Notes, 98:2 (2015), 265–272  isi  scopus
4. L. S. Kazarin, “On Ditsman's lemma”, Trudy Inst. Mat. i Mekh. UrO RAN, 19:3 (2013),  150–157  mathnet  mathscinet  elib; Proc. Steklov Inst. Math. (Suppl.), 285, suppl. 1 (2014), S91–S98  isi  scopus
5. B. Amberg, L. S. Kazarin, “$ABA$-groups with cyclic subgroup $B$”, Trudy Inst. Mat. i Mekh. UrO RAN, 18:3 (2012),  10–22  mathnet  elib
6. E. S. Garipova, L. S. Kazarin, “On the finite near-rings generated by endomorphisms of an extra-special 2-group”, Diskr. Mat., 22:1 (2010),  104–114  mathnet  mathscinet  zmath  elib; Discrete Math. Appl., 20:1 (2010), 113–125
7. L. S. Kazarin, E. I. Chankov, “Finite simply reducible groups are soluble”, Mat. Sb., 201:5 (2010),  27–40  mathnet  mathscinet  zmath  elib; Sb. Math., 201:5 (2010), 655–668  isi  elib  scopus
8. L. S. Kazarin, E. I. Chankov, “A commutativity criterion for a group of odd order”, Model. Anal. Inform. Sist., 16:2 (2009),  103–108  mathnet
9. V. M. Sidel'nikov, L. S. Kazarin, “On a group algebra of a dihedral group and complexity of multiplication of second order matrices”, Tr. Diskr. Mat., 11:1 (2008),  109–118  mathnet
10. L. S. Kazarin, “Finite groups with factorization”, Tr. Inst. Mat., 16:1 (2008),  40–46  mathnet
11. L. S. Kazarin, V. V. Yanishevskii, “On finite simply reducible groups”, Algebra i Analiz, 19:6 (2007),  86–116  mathnet  mathscinet  zmath; St. Petersburg Math. J., 19:6 (2008), 931–951  isi
12. L. S. Kazarin, V. M. Sidel'nikov, “An automorphism group of Suzuki $p$-group”, Tr. Diskr. Mat., 10 (2007),  87–96  mathnet
13. L. S. Kazarin, “Nilpotent algebras and their applications”, Trudy Inst. Mat. i Mekh. UrO RAN, 13:1 (2007),  102–114  mathnet  mathscinet  elib; Proc. Steklov Inst. Math. (Suppl.), 257, suppl. 1 (2007), S86–S99  scopus
14. L. S. Kazarin, V. M. Sidel'nikov, “On the automorphism group of a Suzuki $p$-algebra”, Mat. Zametki, 80:4 (2006),  526–535  mathnet  mathscinet  zmath  elib; Math. Notes, 80:4 (2006), 500–508  isi  scopus
15. L. S. Kazarin, V. M. Sidel'nikov, “On an approach to the quantum codes design”, Tr. Diskr. Mat., 8 (2004),  128–138  mathnet
16. B. Amberg, L. S. Kazarin, “On the Dimension of Nilpotent Algebras”, Mat. Zametki, 70:4 (2001),  483–490  mathnet  mathscinet  zmath; Math. Notes, 70:4 (2001), 439–446  isi
17. L. S. Kazarin, I. A. Sagirov, “On degrees of irreducible characters of finite simple groups”, Trudy Inst. Mat. i Mekh. UrO RAN, 7:2 (2001),  113–123  mathnet  mathscinet  zmath  elib; Proc. Steklov Inst. Math. (Suppl.), 2001no. , suppl. 2, S71–S81
18. B. Amberg, L. S. Kazarin, “On minimal nilpotent algebras of a given nilpotency class”, Trudy Inst. Mat. i Mekh. UrO RAN, 7:2 (2001),  17–26  mathnet  mathscinet  zmath  elib; Proc. Steklov Inst. Math. (Suppl.), 2001no. , suppl. 2, S16–S25
19. B. Amberg, L. S. Kazarin, B. Hoefling, “Finite groups with multiple factorizations”, Fundam. Prikl. Mat., 4:4 (1998),  1251–1263  mathnet  mathscinet  zmath
20. L. S. Kazarin, “On the groups proposed by Sidel'nikov”, Mat. Sb., 189:7 (1998),  131–144  mathnet  mathscinet  zmath; Sb. Math., 189:7 (1998), 1087–1100  isi  scopus
21. D. L. Zagorin, L. S. Kazarin, “Abelian $ABA$-factorizations of finite groups”, Dokl. Akad. Nauk, 347:5 (1996),  590–592  mathnet  mathscinet  zmath
22. O. A. Zharov, L. S. Kazarin, “Towards a Theory of Group Convolution”, Probl. Peredachi Inf., 29:3 (1993),  104–106  mathnet  mathscinet  zmath; Problems Inform. Transmission, 29:3 (1993), 292–294
23. L. S. Kazarin, L. A. Kurdachenko, “Finiteness conditions and factorizations in infinite groups”, Uspekhi Mat. Nauk, 47:3(285) (1992),  75–114  mathnet  mathscinet  zmath; Russian Math. Surveys, 47:3 (1992), 81–126  isi
24. L. S. Kazarin, “Burnside's $p^\alpha$-lemma”, Mat. Zametki, 48:2 (1990),  45–48  mathnet  mathscinet  zmath; Math. Notes, 48:2 (1990), 749–751  isi
25. L. S. Kazarin, “On a problem of Szép”, Izv. Akad. Nauk SSSR Ser. Mat., 50:3 (1986),  479–507  mathnet  mathscinet  zmath; Math. USSR-Izv., 28:3 (1987), 467–495
26. L. S. Kazarin, “Finite groups containing a $TI$-subgroup”, Izv. Vyssh. Uchebn. Zaved. Mat., 1985, 9,  66–68  mathnet  mathscinet  zmath
27. L. S. Kazarin, “On the product of finite groups”, Dokl. Akad. Nauk SSSR, 269:3 (1983),  528–531  mathnet  mathscinet  zmath
28. L. S. Kazarin, “Automorphisms, factorizations and theorems of Sylow-type theorems”, Mat. Sb. (N.S.), 120(162):2 (1983),  190–199  mathnet  mathscinet  zmath; Math. USSR-Sb., 48:1 (1984), 183–192
29. L. S. Kazarin, “On groups with factorization”, Dokl. Akad. Nauk SSSR, 256:1 (1981),  26–29  mathnet  mathscinet  zmath
30. L. S. Kazarin, “On groups with isolated conjugacy classes”, Izv. Vyssh. Uchebn. Zaved. Mat., 1981, 7,  40–45  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 25:7 (1981), 43–49
31. L. S. Kazarin, “Tests for the nonsimplicity of factorable groups”, Izv. Akad. Nauk SSSR Ser. Mat., 44:2 (1980),  288–308  mathnet  mathscinet  zmath; Math. USSR-Izv., 16:2 (1981), 261–278  isi
32. L. S. Kazarin, Yu. A. Korzyukov, “Finite solvable groups with supersolvable maximal subgroups”, Izv. Vyssh. Uchebn. Zaved. Mat., 1980, 5,  22–27  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 24:5 (1980), 23–29
33. L. S. Kazarin, “On the product of two groups that are close to being nilpotent”, Mat. Sb. (N.S.), 110(152):1(9) (1979),  51–65  mathnet  mathscinet  zmath; Math. USSR-Sb., 38:1 (1981), 47–59  isi
34. L. S. Kazarin, “Groups with restrictions on the normalizers of subgroups”, Izv. Vyssh. Uchebn. Zaved. Mat., 1973, 2,  41–50  mathnet  mathscinet  zmath
35. L. S. Kazarin, “On some classes of finite groups”, Dokl. Akad. Nauk SSSR, 197:4 (1971),  773–776  mathnet  mathscinet  zmath

36. D. N. Akhiezer, È. B. Vinberg, V. V. Gorbatsevich, L. S. Kazarin, D. A. Leites, A. M. Lukatskii, A. N. Shchetinin, “Arkadii L'vovich Onishchik (obituary)”, Uspekhi Mat. Nauk, 75:4(454) (2020),  195–206  mathnet; Russian Math. Surveys, 75:4 (2020), 765–777  isi
37. D. N. Akhiezer, È. B. Vinberg, V. V. Gorbatsevich, V. G. Durnev, R. Zulanke, L. S. Kazarin, D. A. Leites, V. V. Serganova, V. M. Tikhomirov, “Arkadii L'vovich Onishchik (on his 70th birthday)”, Uspekhi Mat. Nauk, 58:6(354) (2003),  193–200  mathnet  mathscinet  zmath; Russian Math. Surveys, 58:6 (2003), 1245–1253  isi
38. L. S. Kazarin, A. I. Kostrikin, “School on Theory of Finite Groups”, Uspekhi Mat. Nauk, 44:3(267) (1989),  196–197  mathnet

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