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1.
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
2.
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
3.
Orderable solvable groups in which every relatively convex subgroup is normal are studied. If such a class is subgroup closed
than it is precisely the class of solvable orderable groups which are locally of finite (Mal’tsev) rank. A criterion for an
orderable metabelian group to have every relatively convex subgroup normal is given. Examples of an orderable solvable group
G of length three with periodic G/G′ and of an orderable solvable group of length four with only one proper normal relatively convex subgroup are constructed.
To the memory of N. Ya. Medvedev
Supported by RFBR (project No. 03-01-00320).
Translated from Algebra i Logika, Vol. 48, No. 3, pp. 291–308, May–June, 2009. 相似文献
4.
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
5.
Let {ie166-01} be a set of finite groups. A group G is said to be saturated by the groups in {ie166-02} if every finite subgroup
of G is contained in a subgroup isomorphic to a member of {ie166-03}. It is proved that a periodic group G saturated by groups
in a set {U3(2m) | m = 1, 2, …} is isomorphic to U3(Q) for some locally finite field Q of characteristic 2; in particular, G is locally finite.
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Translated from Algebra i Logika, Vol. 47, No. 3, pp. 288–306, May–June, 2008. 相似文献
6.
In the paper it is proved that the projective groupL
2(q) cannot be the automorphism group of a finite left distributive quasigroup. This is a special case of the conjecture according
to which the automorphism group of a left distributive quasigroup is solvable.
Translated fromMatematicheskie Zametki, Vol. 63, No. 5, pp. 725–728, May, 1998. 相似文献
7.
A. S. Kondratev 《Siberian Mathematical Journal》2007,48(6):1001-1018
We prove that if L is one of the simple groups E
6(q) and 2
E
6(q) and G is some finite group with the same spectrum as L, then the commutant of G/F(G) is isomorphic to L and the quotient G/G′ is a cyclic {2,3}-group.
Original Russian Text Copyright ? 2007 Kondrat’ev A. S.
The author was supported by the Russian Foundation for Basic Research (Grant 04-01-00463) and the RFBR-NSFC (Grant 05-01-39000).
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 48, No. 6, pp. 1250–1271, November–December, 2007. 相似文献
8.
Two groups are said to be isospectral if they share the same set of element orders. For every finite simple linear group L
of dimension n over an arbitrary field of characteristic 2, we prove that any finite group G isospectral to L is isomorphic
to an automorphic extension of L. An explicit formula is derived for the number of isomorphism classes of finite groups that
are isospectral to L. This account is a continuation of the second author's previous paper where a similar result was established
for finite simple linear groups L in a sufficiently large dimension (n > 26), and so here we confine ourselves to groups of
dimension at most 26.
Supported by RFBR (project Nos. 08-01-00322 and 06-01-39001), by SB RAS (Integration Project No. 2006.1.2), and by the Council
for Grants (under RF President) and State Aid of Leading Scientific Schools (grant NSh-344.2008.1) and Young Doctors and Candidates
of Science (grants MD-2848.2007.1 and MK-377.2008.1).
Translated from Algebra i Logika, Vol. 47, No. 5, pp. 558–570, September–October, 2008. 相似文献
9.
A. V. Zavarnitsin 《Algebra and Logic》2006,45(2):106-116
An exhaustive solution is given to the recognition-by-spectrum problem for finite, simple, three-dimensional unitary groups.
For every such group, the number of non-isomorphic, finite, isospectral groups is determined. In particular, a new counterexample
to Problem 13.63 in the Kourovka Notebook is furnished.
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. 2, pp. 185–202, March–April, 2006. 相似文献
10.
D. O. Revin 《Algebra and Logic》2008,47(3):210-227
11.
A. I. Budkin 《Algebra and Logic》2008,47(5):304-313
Let A be a universal algebra and H its subalgebra. The dominion of H in A (in a class {ie304-01}) is the set of all elements
a ∈ A such that every pair of homomorphisms f, g: A → ∈ {ie304-02} satisfies the following: if f and g coincide on H, then
f(a) = g(a). A dominion is a closure operator on a set of subalgebras of a given algebra. The present account treats of closed
subalgebras, i.e., those subalgebras H whose dominions coincide with H. We introduce projective properties of quasivarieties
which are similar to the projective Beth properties dealt with in nonclassical logics, and provide a characterization of closed
algebras in the language of the new properties. It is also proved that in every quasivariety of torsion-free nilpotent groups
of class at most 2, a divisible Abelian subgroup H is closed in each group 〈H, a〉 generated by one element modulo H.
Translated from Algebra i Logika, Vol. 47, No. 5, pp. 541–557, September–October, 2008. 相似文献
12.
V. A. Roman'kov 《Algebra and Logic》2007,46(1):37-45
It is proved that in any finite representation of any finitely generated nilpotent group of nilpotency class l ⩾ 1, the averaged
Dehn function σ(n) is subasymptotic w.r.t. the function nl+1. As a consequence it is stated that in every finite representation of a free nilpotent group of nilpotency class l of finite
rank r ⩾ 2, the Dehn function σ(n) is Gromov subasymptotic.
Supported by RFBR grant No. 04-01-00489.
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Translated from Algebra i Logika, Vol. 46, No. 1, pp. 60–74, January–February, 2007. 相似文献
13.
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
14.
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
15.
E. I. Timoshenko 《Algebra and Logic》2006,45(4):254-260
It is proved that test rank of a free solvable non-Abelian group of finite rank is 1 less than the rank of that group. This
gives the answer to Question 14.88 posed in the Kourovka Notebook by Fine and Shpilrain, asking whether or not a free solvable
group of rank 2 and solvability index n ≥ 3 has test elements.
Supported by RFBR grant No. 05-01-00292.
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Translated from Algebra i Logika, Vol. 45, No. 4, pp. 447–457, July–August, 2006. 相似文献
16.
K. V. Kostousov 《Algebra and Logic》2008,47(2):118-124
We point out a countable set of pairwise nonisomorphic Cayley graphs of the group ℤ4 that are limit for finite minimal vertex-primitive graphs admitting a vertex-primitive automorphism group containing a regular
Abelian normal subgroup.
Supported by RFBR grant No. 06-01-00378.
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Translated from Algebra i Logika, Vol. 47, No. 2, pp. 203–214, March–April, 2008. 相似文献
17.
It is proved that if L is one of the simple groups 3D4(q) or F4(q), where q is odd, and G is a finite group with the set of element orders as in L, then the derived subgroup of G/F(G) is
isomorphic to L and the factor group G/G′ is a cyclic {2, 3}-group.
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Translated from Algebra i Logika, Vol. 44, No. 5, pp. 517–539, September–October, 2005.
Supported by RFBR grant No. 04-01-00463. 相似文献
18.
V. V. Bludov 《Algebra and Logic》2005,44(6):370-380
We give examples of linearly ordered groups that are not embeddable in divisible orderable. In the first example, the group
does not embed in any divisible group with strictly isolated unity. In the second example, the group in question is an O*-group,
and in the third, it is a group with a central system of convex subgroups.
To my teacher A. I. Kokorin
Supported by RFBR grant Nos. 96-01-00358, 99-01-00335, and 03-01-00320.
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Translated from Algebra i Logika, Vol. 44, No. 6, pp. 664–681, November–December, 2005. 相似文献
19.
S. A. Zyubin 《Algebra and Logic》2006,45(5):296-305
A subgroup having non-empty intersection with each class of conjugate elements of the group is said to be conjugately dense.
It is shown that, under certain conditions, the number of conjugately dense subgroups in a free product with amalgamation
is not less than some cardinal. As a consequence, P. Neumann’s conjecture in the Kourovka notebook (Question 6.38) is refuted.
It is also stated that a modular group and a non-Abelian group of countable or finite rank possess continuum many pairwise
non-conjugate conjugately dense subgroups.
Supported by RFBR grant No. 03-01-00905.
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Translated from Algebra i Logika, Vol. 45, No. 5, pp. 520–537, September–October, 2006. 相似文献
20.
A number of conditions are specified which are sufficient for totally ordered groups with polycyclic factor group to contain
a finite normal series of convex subgroups whose factors possess good enough properties. In any case studying such totally
ordered groups is reduced to treating extensions of these groups as well as their virtually o-equivalent extensions. The concept
of a virtually o-equivalent extension is a particular case of the notion of an Archimedean extension.
Supported by RFBR project No. 03-01-00320.
Translated from Algebra i Logika, Vol. 47, No. 5, pp. 529–540, September–October, 2008. 相似文献