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1.
A. V. Zavarnitsine 《Algebra and Logic》2006,45(4):220-231
We obtain the first example of an infinite series of finite simple groups that are uniquely determined by their prime graph
in the class of all finite groups. We also show that there exist almost simple groups for which the number of finite groups
with the same prime graph is equal to 2.
Supported by RFBR grant No. 05-01-00797, and by SB RAS Young Researchers Support grant No. 29 and Integration project No.
2006.1.2.
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Translated from Algebra i Logika, Vol. 45, No. 4, pp. 390–408, July–August, 2006. 相似文献
2.
A. V. Vasilyev 《Algebra and Logic》1998,37(1):9-20
A minimal permutation representation of a group is its faithful permutation representation of least degree. Here the minimal
permutation representations of finite simple exceptional twisted groups are studied: their degrees and point stabilizers,
as well as ranks, subdegrees, and double stabilizers, are found. We can thus assert that, modulo the classification of finite
simple groups, the aforesaid parameters are known for all finite simple groups.
Supported by RFFR grant No. 96-01-01893, through the program “Universities of Russia”, and by grant No. RPC300 of ISF and
the Government of Russia.
Translated fromAlgebra i Logika, Vol. 37, No. 1, pp. 17–35, January–February, 1998. 相似文献
3.
V. I. Zenkov 《Algebra and Logic》1996,35(3):160-163
Using the basic theorem on the classification of finite simple groups, we answer one of the questions concerning the generation
of finite groups by the class of conjugate Abelian subgroups.
Supported by RFFR grant No. 93-01-01529.
Translated fromAlgebra i Logika, Vol. 35, No. 3, pp. 288–293, May–June, 1996. 相似文献
4.
A. V. Vasilyev 《Algebra and Logic》1996,35(6):371-383
A minimal permutation representation of a group is a faithful permutation representation of least degree. Well-studied to
date are the minimal permutation representations of finite sporadic and classical groups for which degrees, point stabilizers,
as well as ranks, subdegrees, and double stabilizers, have been found. Here we attempt to provide a similar account for finite
simple ezceptional groups of types G2 and F4.
Supported by RFFR grant No. 96-01-01893, the program “Universities of Russia,” and by International Science Foundation and
Government of Russia grant No. RPC300.
Translated fromAlgebra i Logika, Vol. 35, No. 6, pp. 663–684, November–December, 1996. 相似文献
5.
For every finite non-Abelian simple group, we give an exhaustive arithmetic criterion for adjacency of vertices in a prime
graph of the group. For the prime graph of every finite simple group, this criterion is used to determine an independent set
with a maximal number of vertices and an independent set with a maximal number of vertices containing 2, and to define orders
on these sets; the information obtained is collected in tables. We consider several applications of these results to various
problems in finite group theory, in particular, to the recognition-by-spectra problem for finite groups.
Supported by RFBR grant No. 05-01-00797; by the Council for Grants (under RF President) and State Aid of Fundamental Science
Schools, project NSh-2069.2003.1; by the RF Ministry of Education Developmental Program for Scientific Potential of the Higher
School of Learning, project No. 8294; by FP “Universities of Russia,” grant No. UR.04.01.202; and by Presidium SB RAS grant
No. 86-197.
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Translated from Algebra i Logika, Vol. 44, No. 6, pp. 682–725, November–December, 2005. 相似文献
6.
E. P. Vdovin 《Algebra and Logic》2000,39(5):301-312
Orders and the structure of large nilpotent subgroups in all finite simple groups are determined. In particular, it is proved
that if G is a finite simple non-Abelian group, and N is some of its nilpotent subgroups, then |N|2<|G|.
Supported through FP “Integration” project No. 274, by RFFR grant No. 99-01-00550, by International Soros Education Program
for Exact Sciences (ISEP) grant No. S99-56, and by a SO RAN grant for Young Scientists, Presidium Decree No. 83 of 03/10/2000.
Translated fromAlgebra i Logika, Vol. 39, No. 5, pp. 526–546, September—October, 2000. 相似文献
7.
Non-nilpotent, finitely generated, associative nil-algebras are studied as well as their adjoint groups and Golod groups.
Solutions are given to some problems in residually finite group theory, questions posed in the Kourovka Notebook included.
Supported by RFBR grant No. 03-01-00356.
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Translated from Algebra i Logika, Vol. 45, No. 2, pp. 231–238, March–April, 2006. 相似文献
8.
A. V. Vasilyev 《Algebra and Logic》1997,36(5):302-310
A minimal permutation representation of a group is its faithful permutation representation of least degree. We will find degrees
and point stabilizers, as well as ranks, subdegrees, and double stabilizers, for groups of types E6, E7, and E8. This brings to a close the study of minimal permutation representations of finite simple Chevalley groups.
Supported by RFFR grant No. 93-01-01501, through the program “Universities of Russia,” and by grant No. RPC300 of ISF and
the Government of Russia.
Translated fromAlgebra i Logika, Vol. 36, No. 5, pp. 518–530, September–October, 1997. 相似文献
9.
E. P. Vdovin 《Algebra and Logic》2007,46(2):90-119
In the paper we work to complete the classification of Carter subgroups in finite almost simple groups. In particular, it
is proved that Carter subgroups of every finite almost simple group are conjugate. Based on our previous results, together
with those obtained by F. Dalla Volta, A. Lucchini, and M. C. Tamburini, as a consequence we derive that Carter subgroups
of every finite group are conjugate.
Supported by RFBR grant No. 05-01-00797; by the Council for Grants (under RF President) for Support of Young Russian Scientists
via projects MK-1455.2005.1 and MK-3036.2007.1; by SB RAS Young Researchers Support grant No. 29; via Integration Project
No. 2006.1.2.
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Translated from Algebra i Logika, Vol. 46, No. 2, pp. 157–216, March–April, 2007. 相似文献
10.
It is proved that a finite group isomorphic to a simple non-Abelian group L3(2m) or U3(2m) is, up to isomorphism, recognizable by a set of its element orders. On the other hand, for every simple group S=S4(2m), there exist infinitely many pairwise non-isomorphic groups G with w(G)=w(S). As a consequence, we present a list of all
recognizable finite simple groups G, for which 4t ∉ ω(G) with t>1.
Supported by RFFR grant No. 99-01-00550, by the National Natural Science Foundation of China (grant No. 19871066), and by
the State Education Ministry of China (grant No. 98083).
Translated fromAlgebra i Logika, Vol. 39, No. 5, pp. 567–585, September–October, 2000. 相似文献
11.
Maximal tori of all finite simple classical groups, as well as of special and general projective linear and unitary groups,
are treated. For every such torus, its expression as a direct sum of cyclic groups is obtained in an explicit form.
Supported by RFBR grant Nos. 05-01-00797 and 06-01-39001, and by SB RAS Integration Project No. 2006.1.2.
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Translated from Algebra i Logika, Vol. 46, No. 2, pp. 129–156, March–April, 2007. 相似文献
12.
13.
Finite groups of Lie type form the greater part of known finite simple groups. An important class of subgroups of finite groups
of Lie type are so-called reductive subgroups of maximal rank. These arise naturally as Levi factors of parabolic groups and
as centralizers of semisimple elements, and also as subgroups with maximal tori. Moreover, reductive groups of maximal rank
play an important part in inductive studies of subgroup structure of finite groups of Lie type. Yet a number of vital questions
dealing in the internal structure of such subgroups are still not settled. In particular, we know which quasisimple groups
may appear as central multipliers in the semisimple part of any reductive group of maximal rank, but we do not know how normalizers
of those quasisimple groups are structured. The present paper is devoted to tackling this problem.
Supported by RFBR (grant No. 05-01-00797) and by SB RAS (Young Researchers Support grant No. 29 and Integration project No.
2006.1.2).
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Translated from Algebra i Logika, Vol. 47, No. 1, pp. 3–30, January–February, 2008. 相似文献
14.
D. O. Revin 《Algebra and Logic》2008,47(3):210-227
15.
V. D. Mazurov 《Algebra and Logic》2000,39(1):42-49
The article contains two characterizations of projective linear groups PGL2(P) over a locally finite field P of characteristic 2: the first is defined in terms of permutation groups, and the second,
in terms of a structure of involution centralizers. One of the two is used to prove the existence of infinite groups which
are recognizable by the set of their element orders.
In memory of Viktor A. Gorbunov
Supported by RFFR grant No. 99-01-00550.
Translated fromAlgebra i Logika, Vol. 39, No. 1, pp. 74–86, January–February, 2000. 相似文献
16.
It is proved that finite simple groups L4(2m), m ⩾ 2, and U4(2m), m ⩾ 2, are, up to isomorphism, recognized by spectra, i.e., sets of their element orders, in the class of finite groups.
As a consequence the question on recognizability by spectrum is settled for all finite simple groups without elements of order
8.
Supported by RFBR (grant Nos. 05-01-00797 and 06-01-39001), by SB RAS (Complex Integration project No. 1.2), and by the Ministry
of Education of China (Project for Retaining Foreign Expert).
Supported by NSF of Chongqing (CSTC: 2005BB8096).
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Translated from Algebra i Logika, Vol. 47, No. 1, pp. 83–93, January–February, 2008. 相似文献
17.
Centers of universal envelopes for Mal’tsev algebras are explored. It is proved that the center of the universal envelope
for a finite-dimensional semisimple Mal’tsev algebra over a field of characteristic 0 is a ring of polynomials in a finite
number of variables equal to the dimension of its Cartan subalgebra, and that universal enveloping algebra is a free module
over its center. Centers of universal enveloping algebras are computed for some Mal’tsev algebras of small dimensions.
Supported by FAPESP grant No. 04/08537-4 and by SO RAN grant No. 1.9.
Supported by FAPESP grant Nos. 05/60142-7, 05/60337-2 and by CNPq grant No. 304991/2006-6.
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Translated from Algebra i Logika, Vol. 46, No. 5, pp. 560–584, September–October, 2007. 相似文献
18.
Spectra of finite linear and unitary groups 总被引:1,自引:0,他引:1
A. A. Buturlakin 《Algebra and Logic》2008,47(2):91-99
The spectrum of a finite group is the set of its element orders. An arithmetic criterion determining whether a given natural
number belongs to a spectrum of a given group is furnished for all finite special, projective general, and projective special
linear and unitary groups.
Supported by RFBR (grant Nos. 08-01-00322 and 06-01-39001) and by the Council for Grants (under RF President) and State Aid
of Leading Scientific Schools (project NSh-344.2008.1).
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Translated from Algebra i Logika, Vol. 47, No. 2, pp. 157–173, March–April, 2008. 相似文献
19.
V. G. Bardakov 《Algebra and Logic》1997,36(5):288-301
We study into widths of verbal subgroups of HNN-extensions, and of groups with one defining relation. It is proved that if
a group G* is an HNN-extension and the connected subgroups in G* are distinct from a base of the extension, then every verbal subgroup V(G*) has infinite width relative to a finite proper set V of words. A similar statement is proven to hold for groups presented
by one defining relation and ≥3 generators.
to Yurii I. Merzlyakov dedicated
Supported by RFFR grant No. 93-01-01513.
Translated fromAlgebra i Logika, Vol. 36, No. 5, pp. 494–517, September–October, 1997. 相似文献
20.
K. N. Ponomarev 《Algebra and Logic》1998,37(1):35-47
An analog of the Abhyankar lemma is proved for an arbitrary finite separable extensions of discretely valued fields with a
functional residue field.
Supported by RFFR grants Nos. 96-01-01675 and 96-01-01678, and by RF Goskomvuz grant No. 2.
Translated fromAlgebra i Logika, Vol. 37, No. 1, pp. 63–87., January–February, 1998. 相似文献