共查询到20条相似文献,搜索用时 0 毫秒
1.
Houshang Behravesh Mohammad Hossein Jafari 《数学物理学报(B辑英文版)》2007,27(2):297-300
The quantities c(G), q(G) and p(G) for finite groups were defined by H. Behravesh. In this article, these quantities for the alternating group An and the symmetric group Sn are calculated. It is shown that c(G) = q(G)=p(G) = n, when G = An or Sn. 相似文献
2.
Ilya Gorshkov 《代数通讯》2019,47(9):3905-3914
3.
Daniela Bubboloni 《Journal of Combinatorial Theory, Series A》2011,118(7):2000-2024
In this paper we investigate the minimum number of maximal subgroups Hi, i=1,…,k of the symmetric group Sn (or the alternating group An) such that each element in the group Sn (respectively An) lies in some conjugate of one of the Hi. We prove that this number lies between a?(n) and bn for certain constants a,b, where ?(n) is the Euler phi-function, and we show that the number depends on the arithmetical complexity of n. Moreover in the case where n is divisible by at most two primes, we obtain an upper bound of 2+?(n)/2, and we determine the exact value for Sn when n is odd and for An when n is even. 相似文献
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L. N. Vaserstein 《K-Theory》1989,2(5):647-673
We consider a module with an alternating form over a commutative ring. Under certain conditions, which hold, for example, when the form is nonsingular and the module is projective of rank 6 and contains a unimodular vector, we describe all subgroups of the symplectic group which are normalized by symplectic transvections. This generalizes many previous results of Dickson, Klingenberg, Abe, Bak, et al. 相似文献
6.
Alexander S. Kleshchev Pham Huu Tiep 《Transactions of the American Mathematical Society》2004,356(5):1971-1999
Let be an algebraically closed field of characteristic and be an almost simple group or a central extension of an almost simple group. An important problem in representation theory is to classify the subgroups of and -modules such that the restriction is irreducible. For example, this problem is a natural part of the program of describing maximal subgroups in finite classical groups. In this paper we investigate the case of the problem where is the Schur's double cover or .
7.
《Discrete Mathematics》2022,345(6):112834
A Cayley graph is said to be an NNN-graph if its automorphism group contains two isomorphic regular subgroups where one is normal and the other is non-normal. In this paper, we show that there exist NNN-graphs among the Cayley graphs for symmetric groups if and only if . 相似文献
8.
Robert Beals Charles R. Leedham-Green Alice C. Niemeyer Cheryl E. Praeger Á kos Seress 《Transactions of the American Mathematical Society》2003,355(5):2097-2113
We present a Las Vegas algorithm which, for a given black-box group known to be isomorphic to a symmetric or alternating group, produces an explicit isomorphism with the standard permutation representation of the group. This algorithm has applications in computations with matrix groups and permutation groups.
In this paper, we handle the case when the degree of the standard permutation representation is part of the input. In a sequel, we shall treat the case when the value of is not known in advance.
As an important ingredient in the theoretical basis for the algorithm, we prove the following result about the orders of elements of : the conditional probability that a random element is an -cycle, given that , is at least .
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11.
Hideaki Morita 《Advances in Mathematics》2007,212(1):277-292
We consider the Green polynomials at roots of unity. We obtain a recursive formula for the Green polynomials at roots of unity whose orders do not exceed some positive integer. The formula is described in a combinatorial manner. The coefficients of the recursive formula are realized by the cardinality of a set of permutations. The formula gives an interpretation of a combinatorial property on a family of graded modules for the symmetric group in terms of representation theory. 相似文献
12.
In the Atlas of abstract regular polytopes for small almost simple groups by Leemans and Vauthier, the polytopes whose automorphism group is a symmetric group Sn of degree 5?n?9 are available. Two observations arise when we look at the results: (1) for n?5, the (n−1)-simplex is, up to isomorphism, the unique regular (n−1)-polytope having Sn as automorphism group and, (2) for n?7, there exists, up to isomorphism and duality, a unique regular (n−2)-polytope whose automorphism group is Sn. We prove that (1) is true for n≠4 and (2) is true for n?7. Finally, we also prove that Sn acts regularly on at least one abstract polytope of rank r for every 3?r?n−1. 相似文献
13.
Marston D.E Conder 《Journal of Combinatorial Theory, Series B》1985,39(2):179-186
The symmetric genus of a finite group G has been defined by Thomas W. Tucker as the smallest genus of all surfaces on which G acts faithfully as a group of automorphisms (some of which may reverse the orientation of the surface). This note announces the symmetric genus of all finite alternating and symmetric groups. 相似文献
14.
Norberto Gavioli 《Transactions of the American Mathematical Society》1997,349(7):2969-2980
In this paper there are found necessary and sufficient conditions that a pair of solvable finite groups, say and , must satisfy for the existence of a solvable finite group containing two isomorphic copies of and inducing the same permutation character. Also a construction of is given as an iterated wreath product, with respect to their actions on their natural modules, of finite one-dimensional affine groups.
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AbstractIn this paper, we introduce the concept of sse-embedded subgroups of finite groups and present some new characterizations of solubility of finite groups using the sse-embedding property of subgroups. Furthermore, we discuss the sse-embedded subgroups in finite nonabelian simple groups. Some previously known results are generalized and unified. 相似文献
17.
Let G be a finite group,and H a subgroup of G.H is called s-permutably embedded in G if each Sylow subgroup of H is a Sylow subgroup of some s-permutable subgroup of G.In this paper,we use s-permutably embedding property of subgroups to characterize the p-supersolvability of finite groups,and obtain some interesting results which improve some recent results. 相似文献
18.
Fix an integern≧3. We show that the alternating groupA
n appears as Galois group over any Hilbertian field of characteristic different from 2. In characteristic 2, we prove the same
whenn is odd. We show that any quadratic extension of Hilbertian fields of characteristic different from 2 can be embedded in anS
n-extension (i.e. a Galois extension with the symmetric groupS
n as Galois group). Forn≠6, it will follow thatA
n has the so-called GAR-property over any field of characteristic different from 2. Finally, we show that any polynomialf=X
n+…+a1X+a0 with coefficients in a Hilbertian fieldK whose characteristic doesn’t dividen(n-1) can be changed into anS
n-polynomialf
* (i.e the Galois group off
* overK Gal(f
*, K), isS
n) by a suitable replacement of the last two coefficienta
0 anda
1. These results are all shown using the Newton polygon.
The author acknowledges the financial support provided through the European Community’s Human Potential Programme under contract
HPRN-CT-2000-00114, GTEM. 相似文献
19.
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).
20.
Robert M. Guralnick 《Journal of Combinatorial Theory, Series A》2006,113(7):1243-1256
Each group G of n×n permutation matrices has a corresponding permutation polytope, P(G):=conv(G)⊂Rn×n. We relate the structure of P(G) to the transitivity of G. In particular, we show that if G has t nontrivial orbits, then min{2t,⌊n/2⌋} is a sharp upper bound on the diameter of the graph of P(G). We also show that P(G) achieves its maximal dimension of 2(n−1) precisely when G is 2-transitive. We then extend the results of Pak [I. Pak, Four questions on Birkhoff polytope, Ann. Comb. 4 (1) (2000) 83-90] on mixing times for a random walk on P(G). Our work depends on a new result for permutation groups involving writing permutations as products of indecomposable permutations. 相似文献