共查询到20条相似文献,搜索用时 15 毫秒
1.
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
2.
V. V. Korableva 《Algebra and Logic》2010,49(5):416-425
Ranks, degrees, subdegrees, and double stabilizers of permutation representations for finite simple orthogonal groups in odd
dimensions are defined on cosets with respect to maximal parabolic subgroups. 相似文献
3.
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
4.
V. D. Mazurov 《Algebra and Logic》1993,32(3):142-153
This work was supported by the Russian Foundation for Fundamental Research, grant 93-011-1501. 相似文献
5.
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
6.
7.
8.
V. V. Korableva 《Algebra and Logic》2010,49(3):246-255
Ranks, degrees, subdegrees, and double stabilizers of permutation representations for finite symplectic groups are defined
on cosets with respect to maximal parabolic subgroups. 相似文献
9.
10.
V. V. Korableva 《Proceedings of the Steklov Institute of Mathematics》2009,267(1):100-110
The ranks, degrees, subdegrees, and double stabilizers of permutation representations of finite special linear and unitary groups on cosets of parabolic maximal subgroups are found. 相似文献
11.
The spectrum of a finite group is the set of its element orders. Two groups are said to be isospectral if their spectra coincide. We deal with the class of finite groups isospectral to simple and orthogonal groups over a field
of an arbitrary positive characteristic p. It is known that a group of this class has a unique nonabelian composition factor. We prove that this factor cannot be isomorphic
to an alternating or sporadic group. We also consider the case where this factor is isomorphic to a group of Lie type over
a field of the same characteristic p. 相似文献
12.
A. A. Gal’t 《Siberian Mathematical Journal》2010,51(2):193-198
We prove the strong reality of an infinite series of groups and some elements of a special form in the simple real groups. 相似文献
13.
Pablo Spiga 《代数通讯》2018,46(6):2440-2450
Given a finite group R, a graphical regular representation of R is a Cayley graph Γ over R with R = Aut(Γ). In this paper we study graphical regular representations of finite non-abelian simple groups of small valency. 相似文献
14.
B. Sury 《Proceedings of the American Mathematical Society》1999,127(7):1973-1974
We answer affirmatively the following question of Derek Holt: Given integers , can one, in a simple manner, find a finite set and permutations such that has order , has order and has order ? The method of proof enables us to prove more general results (Theorems 2 and 3).
15.
Journal of Algebraic Combinatorics - In this paper we characterize those automorphism groups of colored graphs and digraphs that are abelian as abstract groups. This is done in terms of basic... 相似文献
16.
The permutation representation afforded by a Coxeter group W acting on the cosets of a standard parabolic subgroup inherits many nice properties from W such as a shellable Bruhat order and a flat deformation over ?[q] to a representation of the corresponding Hecke algebra. In this paper we define a larger class of “quasiparabolic” subgroups (more generally, quasiparabolic W-sets), and show that they also inherit these properties. Our motivating example is the action of the symmetric group on fixed-point-free involutions by conjugation. 相似文献
17.
18.
O. A. Alekseeva A. S. Kondrat’ev 《Proceedings of the Steklov Institute of Mathematics》2009,266(Z1):10-23
It is proved that, if G is a finite group that has the same set of element orders as the simple group D
p
(q), where p is prime, p ≥ 5 and q ∈ {2, 3, 5}, then the commutator group of G/F(G) is isomorphic to D
p
(q), the subgroup F(G) is equal to 1 for q = 5 and to O
q
(G) for q ∈ {2, 3}, F(G) ≤ G′, and |G/G′| ≤ 2. 相似文献
19.
O. A. Alekseeva A. S. Kondrat’ev 《Proceedings of the Steklov Institute of Mathematics》2009,266(1):10-23
It is proved that, if G is a finite group that has the same set of element orders as the simple group D p (q), where p is prime, p ≥ 5 and q ∈ {2, 3, 5}, then the commutator group of G/F(G) is isomorphic to D p (q), the subgroup F(G) is equal to 1 for q = 5 and to O q (G) for q ∈ {2, 3}, F(G) ≤ G′, and |G/G′| ≤ 2. 相似文献
20.
V. D. Mazurov 《Algebra and Logic》1988,27(5):350-361
Translated from Algebra i Logika, Vol. 27, No. 5, pp. 562–580, September–October, 1988. 相似文献