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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
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.
P. A. Shreiner 《Algebra and Logic》2007,46(1):62-70
We deal with some issues on automatic recognition of interpolation properties in modal calculi extending the logics S5 and
S4.3.
Supported by RFBR grant No. 06-01-00358 and by INTAS grant No. 04-77-7080.
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Translated from Algebra i Logika, Vol. 46, No. 1, pp. 103–119, January–February, 2007. 相似文献
5.
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
6.
K. N. Ponomarev 《Algebra and Logic》2007,46(4):263-273
Various classes of non-associative algebras possessing the property of being rigid under abstract isomorphisms are studied.
Supported by RFBR grant No. 06-01-00159a.
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Translated from Algebra i Logika, Vol. 46, No. 4, pp. 483–502, July–August, 2007. 相似文献
7.
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
8.
The partial quadrangle PQ(s, t, μ) is an incidence system consisting of points and lines in which every line contains s +
1 points, every point sits on t + 1 lines (two lines meet in at most one point), and the meet of the neighborhoods of any
two non-adjacent points in the collinearity graph is a μ-coclique. We provide a classification for partial quadrangles PQ(s,
t, μ) with t ⩽ 6, and study into their automorphisms.
Supported by RFBR grant No. 05-01-00046 and by RFBR-NSFC grant No. 05-01-39000.
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Translated from Algebra i Logika, Vol. 45, No. 5, pp. 603–619, September–October, 2006. 相似文献
9.
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
10.
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
11.
V. P. Spiridonov 《The Ramanujan Journal》2007,13(1-3):265-283
We give elementary proofs of the univariate elliptic beta integral with bases |q|,|p| < 1 and its multiparameter generalizations to integrals on the A
n
and C
n
root systems. We prove also some new unit circle multiple elliptic beta integrals, which are well defined for |q| = 1, and their p → 0 degenerations.
Dedicated to Richard Askey on the occasion of his seventieth birthday.
2000 Mathematics Subject Classification Primary—33D99, 33E05
This work is supported in part by the Russian Foundation for Basic Research (RFBR) grant no. 03-01-00781. 相似文献
12.
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
13.
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
14.
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
15.
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
16.
It is proved that the exponential growth rate of identities in any superalgebra with a nilpotent commutator subalgebra over
a field of zero characteristic is an integer.
Supported by RFBR (project Nos. 07-01-00080 and 06-01-00485) and by the Council for Grants (under RF President) and State
Aid of Leading Scientific Schools (grant NSh-1983.2008.1).
Translated from Algebra i Logika, Vol. 47, No. 5, pp. 617–645, September–October, 2008. 相似文献
17.
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
18.
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
19.
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
20.
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