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1.
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
2.
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
3.
We investigate differences in isomorphism types for Rogers semilattices of computable numberings of families of sets lying
in different levels of the arithmetical hierarchy.
Supported by RFBR grant No. 05-01-00819 and by INTAS grant No. 00-499.
Supported by NSFC grant No. 60310213.
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Translated from Algebra i Logika, Vol. 45, No. 6, pp. 637–654, November–December, 2006. 相似文献
4.
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
5.
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
6.
V. A. Belonogov 《Algebra and Logic》2007,46(1):1-15
We show that treating of (non-trivial) pairs of irreducible characters of the group Sn sharing the same set of roots on one of the sets An and Sn \ An is divided into three parts. This, in particular, implies that any pair of such characters χα and χβ (α and β are respective partitions of a number n) possesses the following property: lengths d(α) and d(β) of principal diagonals
of Young diagrams for α and β differ by at most 1.
Supported by RFBR grant No. 04-01-00463 and by RFBR-NSFC grant No. 05-01-39000.
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Translated from Algebra i Logika, Vol. 46, No. 1, pp. 3–25, January–February, 2007. 相似文献
7.
V. N. Zhelyabin 《Algebra and Logic》1996,35(5):296-304
The notion of a structurable coalgebra is defined. It is proved that every structurable coalgebra is locally finite-dimensional.
Supported by RFFR grant No. 95-01-01356 and by ISF grant No. RB 6000.
Translated fromAlgebra i Logika, Vol. 35, No. 5, pp. 529–542, September–October, 1996. 相似文献
8.
It is shown that polynilpotent groups with a single primitive defining relation have a decidable word problem.
Supported by RFBR grant No. 05-01-00292.
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Translated from Algebra i Logika, Vol. 45, No. 1, pp. 28–43, January–February, 2006. 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.
A. P. Pozhidaev 《Algebra and Logic》2008,47(2):139-152
This account is a first step toward a classification of finite-dimensional simple Filippov superalgebras over an algebraically
closed field of characteristic 0. Here, n-ary Filippov superalgebras with nonzero even and odd parts are treated for the case
n ⩾ 3.
Supported by RFBR (grant No. 05-01-00230) and by SB RAS (Integration project No. 1.9 and Young Researchers Support grant No.
29).
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Translated from Algebra i Logika, Vol. 47, No. 2, pp. 240–261, March–April, 2008. 相似文献
11.
V. A. Belonogov 《Algebra and Logic》2008,47(2):77-90
Previously, we dubbed the conjecture that the alternating group An has no semiproportional irreducible characters for any natural n [1]. This conjecture was then shown to be equivalent to
the following [3]. Let α and β be partitions of a number n such that their corresponding characters χα and χβ in the group Sn are semiproportional on An. Then one of the partitions α or β is self-associated. Here, we describe all pairs (α, β) of partitions satisfying the hypothesis
and the conclusion of the latter conjecture.
Supported by RFBR (grant No. 07-01-00148) and by RFBR-NSFC (grant No. 05-01-39000).
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Translated from Algebra i Logika, Vol. 47, No. 2, pp. 135–156, March–April, 2008. 相似文献
12.
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
13.
A. I. Karol 《Mathematical Notes》1998,63(1):25-32
We construct the asymptotics ast→0 of the trace of the operator exp(−tP) for an elliptic operatorP on a manifold with conical points.
Translated fromMatematicheskie Zametki, Vol. 63, No. 1, pp. 28–36, January, 1998.
This research was supported by the Belarus Foundation for Basic Research under grant No. 96-01 00790. 相似文献
14.
A. Yu. Kolesov 《Mathematical Notes》1998,63(5):614-623
We consider the boundary value problem
. Hereu ∈ ℝ2,D = diag{d
1,d
2},d
1,d
2 > 0, and the functionF is jointly smooth in (u, μ) and satisfies the following condition: for 0 <μ ≪ 1 the boundary value problem has a homogeneous (independent ofx) cycle bifurcating from a loop of the separatrix of a saddle. We establish conditions for stability and instability of this
cycle and give a geometric interpretation of these conditions.
Translated fromMatematicheskie Zametki, Vol. 63, No. 5, pp. 697–708, May, 1998.
This research was supported by the Russian Foundation for Basic Research under grant No. 96-01-00207. 相似文献
15.
L. L. Maksimova 《Algebra and Logic》2008,47(1):56-64
The notions of a weak interpolation property and of weak amalgamation are introduced. It is proved that in varieties with
the congruence extension property, the weak interpolation property is equivalent to the weak amalgamation property. In turn,
weak amalgamability of a variety is equivalent to amalgamability of a class of finitely generated simple algebras in this
variety.
Supported by RFBR (grant Nos. 06-01-00358 and 05-01-04003-NNIOa) and by INTAS (grant No. 04-77-7080).
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Translated from Algebra i Logika, Vol. 47, No. 1, pp. 94–107, January–February, 2008. 相似文献
16.
17.
N. B. Kaygorodov 《Algebra and Logic》2007,46(5):318-329
We describe non-trivial δ-derivations of semisimple finite-dimensional Jordan algebras over an algebraically closed field
of characteristic not 2, and of simple finite-dimensional Jordan superalgebras over an algebraically closed field of characteristic
0. For these classes of algebras and superalgebras, non-zero δ-derivations are shown to be missing for δ ≠ 0, 1/2, 1, and
we give a complete account of 1/2-derivations.
Supported by RFBR grant No. 05-01-00230 and by RF Ministry of Education and Science grant No. 11617.
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Translated from Algebra i Logika, Vol. 46, No. 5, pp. 585–605, September–October, 2007. 相似文献
18.
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
19.
V. M. Murzina 《Algebra and Logic》2007,46(6):409-418
We study into the question whether calculi associated with Ershov topological spaces possess Craig’s interpolation property.
Supported by RFBR grant No. 06-01-00358, by INTAS grant No. 04-77-7080, and by the Council for Grants (under RF President)
and State Aid of Fundamental Science Schools, project NSh-4787.2006.1.
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Translated from Algebra i Logika, Vol. 46, No. 6, pp. 745–762, November–December, 2007. 相似文献
20.
A. A. Makhnev 《Mathematical Notes》2000,68(2):232-236
A set Δ of vertices of a generalized quadrangle of order (s, t) is said to be a hyperoval if any line intersects Δ in either 0, or 2 points. A hyperoval Δ is called an affine ovoid if
|Δ|=2st. It is well known that μ-subgraphs in triangular extensions of generalized quadrangles are hyperovals. In the present paper
we prove that ifS is a triangular extension forGQ(s, t) with totally regular point graph Γ such that μ=2st, thens is even, Γ is an τ-antipodal graph of diameter 3 with τ=1+s/2, and eithers=2, ort=s+2.
Translated fromMatematicheskie Zametki, Vol. 68, No. 2, pp. 266–271, August, 2000. 相似文献