01.01.06 (Mathematical logic, algebra, and number theory)
Birth date:
15.06.1949
E-mail:
, ;
Keywords:
finite groups; group rings; unit groups; integer rings pf algebraic number fields.
Subject:
Main purpose of my investigations is the construction of theory for studying of central units of integral group rings of finite groups. I have the results concerning separate central units and properties of groups of all central units also. Firstly, I obtain the complete descriptions of central unit groups of integral group rings of some finite groups. For investigations of central units I obtain the results about integer rings of abelian fields.
Biography
Graduated from Faculty of Mathematics Novosibirsk State University (NSU) in 1972 (department of algebra and mathematical logic). Ph.D. thesis was defended in 1977. D.Sci. thesis was defended in 2000. A list of my works contains more than 70 titles.
Main publications:
Aleev R. \v{Z}., Higman's central unit theory, units of integral group rings of finite cyclic groups and Fibonacci numbers // Intern. J. of Algebra and Comp. V. 4, no. 3(1994), p. 309–358.
R. Zh. Aleev, O. V. Mitina, A. D. Godova, “Algebraic conjugacy of irreducible characters of a group $GL(2,8)$”, Chelyab. Fiz.-Mat. Zh., 4:2 (2019), 129–141
2018
2.
R. Zh. Aleev, O. V. Mitina, T. A. Khanenko, “Local units of integer group ring of cyclic group of order 64 for character with character field ${\mathbb Q}_{64}$”, Chelyab. Fiz.-Mat. Zh., 3:3 (2018), 253–275
R. Zh. Aleev, M. I. Molodorich, “The unit groups of class character rings of Rudvalis group”, Chelyab. Fiz.-Mat. Zh., 2:2 (2017), 133–151
4.
R. Zh. Aleev, O. V. Mitina, T. A. Khanenko, “Description of the unit group of the integral group ring of a cyclic group of order $16$”, Trudy Inst. Mat. i Mekh. UrO RAN, 23:4 (2017), 32–42
R. Zh. Aleev, O. V. Mitina, T. A. Khanenko, “Finding of units for integer group rings of orders 16 and 32 cyclic groups”, Chelyab. Fiz.-Mat. Zh., 1:4 (2016), 30–55
R. Zh. Aleev, O. V. Mitina, E. A. Khristenko, “Congruence modulo 2 of circular units in the fields $Q_{16}$ and $Q_{32}$”, Chelyab. Fiz.-Mat. Zh., 1:4 (2016), 8–29
R. Zh. Aleev, N. A. Tsybina, “The computation of ranks of unit groups of integral group rings of finite groups”, Vestn. YuUrGU. Ser. Vych. Matem. Inform., 4:1 (2015), 71–85
R. Zh. Aleev, “Small ranks of central unit groups of integral group rings of alternating groups”, Trudy Inst. Mat. i Mekh. UrO RAN, 19:3 (2013), 15–22; Proc. Steklov Inst. Math. (Suppl.), 285, suppl. 1 (2014), S12–S18
2009
9.
R. Zh. Aleev, V. V. Sokolov, “On groups of central units of integral group rings of alternating groups”, Trudy Inst. Mat. i Mekh. UrO RAN, 15:2 (2009), 3–11; Proc. Steklov Inst. Math. (Suppl.), 267, suppl. 1 (2009), S1–S9
R. Zh. Aleev, A. V. Kargapolov, V. V. Sokolov, “The ranks of central unit groups of integral group rings of alternating groups”, Fundam. Prikl. Mat., 14:7 (2008), 15–21; J. Math. Sci., 164:2 (2010), 163–167
R. Zh. Aleev, O. V. Mitina, “The decomposition theorem and ranks of central unit groups of integer group rings of groups $PGL_2(q)$, $q$ odd”, Sib. Èlektron. Mat. Izv., 5 (2008), 652–672
R. Zh. Aleev, V. S. Taksheeva, “Generators of the circular identities group”, Vestnik Chelyabinsk. Gos. Univ., 2008, no. 10, 121–129
2001
13.
R. Zh. Aleev, N. B. Ishechkina, “A theory of central unit groups of integral group rings of groups $Sz(q)$”, Trudy Inst. Mat. i Mekh. UrO RAN, 7:2 (2001), 3–16; Proc. Steklov Inst. Math. (Suppl.), 2001no. , suppl. 2, S1–S15
R. Zh. Aleev, “The Units of Character Fields and the Central Units of Integer Group Rings of Finite Groups”, Mat. Tr., 3:1 (2000), 3–37; Siberian Adv. Math., 11:1 (2001), 1–33
R. Zh. Aleev, G. A. Panina, “The units of cyclic groups of orders 7 and 9”, Izv. Vyssh. Uchebn. Zaved. Mat., 1999, no. 11, 81–84; Russian Math. (Iz. VUZ), 43:11 (1999), 80–83
R. Zh. Aleev, O. V. Peravina, “Ранги групп центральных единиц
целочисленных групповых колец групп $PSL_2(q)$ нечетно”, Vestnik Chelyabinsk. Gos. Univ., 1999, no. 4, 5–15
1981
19.
R. Zh. Aleev, “A condition for a component of the centralizer of an involution to be standard”, Mat. Zametki, 30:2 (1981), 161–170; Math. Notes, 30:2 (1981), 567–571
1980
20.
R. Zh. Aleev, “Fusion-simple finite groups with decomposable Sylow 2-subgroups”, Mat. Zametki, 27:6 (1980), 833–837; Math. Notes, 27:6 (1980), 403–405
1975
21.
R. Zh. Aleev, “Finite groups with decomposable Sylow $2$-subgroups”, Algebra Logika, 14:6 (1975), 611–646
22.
R. Zh. Aleev, “The conjugacy of involutions in finite groups with decomposable
Sylow $2$-subgroups”, Algebra Logika, 14:5 (1975), 491–522
R. Zh. Aleev, V. L. Dil'man, A. D. Drozin, V. I. Zalyapin, V. V. Karachik, A. V. Keller, Yu. M. Kovalev, N. A. Manakova, G. A. Sviridyuk, E. V. Tabarintseva, “Leonid Menikhes (to the $65^{th}$ anniversary)”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 6:3 (2013), 136–140
R. Zh. Aleev, “Higman theory of central units, groups of units of integer group rings of finite cyclic groups, and Fibonacci numbers”, Sibirsk. Mat. Zh., 34:2 (1993), 220
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