共查询到20条相似文献,搜索用时 0 毫秒
1.
2.
Thomas Breuer 《代数通讯》2013,41(9):3173-3176
3.
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).
4.
William M. Kantor 《Journal of Algebraic Combinatorics》2008,28(3):351-363
For several families ℱ of finite transitive permutation groups it is shown that each finite group is isomorphic to a 2-point
stabilizer of infinitely many members of ℱ.
This research was supported in part by NSF grants DMS 9301308 and DMS 0242983. 相似文献
5.
AbstractLet λ(G) be the maximum number of subgroups in an irredundant covering of the finite group G. We prove that if G is a group with λ(G) ≤ 6, then G is supersolvable. We also describe the structure of groups G with λ(G) = 6. Moreover, we show that if G is a group with λ(G)?<?31, then G is solvable. 相似文献
6.
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
7.
For a permutation group given by a set of generators, the problem of finding “special” group members is NP-hard in many cases, e.g., this is true for the problem of finding a permutation with a minimum number of fixed points or a permutation with a minimal Hamming distance from a given permutation. Many of these problems can be modeled as linear optimization problems over permutation groups. We develop a polyhedral approach to this general problem and derive an exact and practically fast algorithm based on the branch & cut-technique. 相似文献
8.
Klaus DENECKE 《中国科学A辑(英文版)》2007,50(5):715-726
Let G be a finite group and S be a finite simple group. In this paper, we prove that if G and S have the same sets of all orders of solvable subgroups, then G is isomorphic to S, or G and S are isomorphic to Bn(q), Cn(q), where n≥3 and q is odd. This gives a positive answer to the problem put forward by Abe and Iiyori. 相似文献
9.
In this paper we present some new results on the connection between the Siegel norm, the length function and irreducible character values of finite groups. In addition, we provide algorithms to compute the length of a cyclotomic integer and the set of cyclotomic integers with Siegel norm bounded by a given positive real number. 相似文献
10.
For a finite group G, let n(G) denote the number of conjugacy classes of non-subnormal subgroups of G. In this paper, we show that a finite group G satisfying n(G)≤2|π(G)| is solvable, and for a finite non-solvable group G, n(G) = 2|π(G)|+1 if and only if G?A5. 相似文献
11.
12.
Thorsten Holm Wolfgang Willems 《Transactions of the American Mathematical Society》2007,359(2):591-603
Recently, a new conjecture on the degrees of the irreducible Brauer characters of a finite group was presented by W. Willems. In this paper we propose a `local' version of this conjecture for blocks of finite groups, giving a lower bound for where the sum runs through the set of irreducible Brauer characters of in terms of invariants of . A slight reformulation leads to interesting open questions about traces of Cartan matrices of blocks.
We show that the local conjecture is true for blocks with one simple module, blocks of -solvable groups and blocks with cyclic defect groups. It also holds for many further examples of blocks of sporadic groups, symmetric groups or groups of Lie type. Finally we prove that the conjecture is true for blocks of tame representation type.
13.
Permutation polynomials over finite fields play important roles in finite fields theory. They also have wide applications in many areas of science and engineering such as coding theory, cryptography, combinatorial design, communication theory and so on. Permutation binomials and permutation trinomials attract people's interest due to their simple algebraic forms and additional extraordinary properties. In this paper, we find a new result about permutation binomials and construct several new classes of permutation trinomials. Some of them are generalizations of known ones. 相似文献
14.
Ryan J. Zerr 《Proceedings of the American Mathematical Society》2006,134(6):1849-1856
Character groups associated with certain dimension groups are considered. It is shown how these character groups can be used to construct an AF groupoid whose dimension group is isomorphic to the original dimension group.
15.
In this paper we prove that a finite group G with Cohen-Macaulay mod p cohomology will have non-trivial undetectable elements in if and only if G is a p-group such that every element of order p in G is central. Applications and examples are also provided.
Received: April 18, 1996 相似文献
16.
Tobias Kildetoft 《代数通讯》2017,45(6):2325-2333
We define the position of an irreducible complex character of a finite group as an alternative to the degree. We then use this to define three classes of groups: position reducible (PR)-groups, inductively position reducible (IPR)-groups and weak IPR-groups. We show that IPR-groups and weak IPR-groups are solvable and satisfy the Taketa inequality (ie, that the derived length of the group is at most the number of degrees of irreducible complex characters of the group), and we show that any M-group is a weak IPR-group. We also show that even though PR-groups need not be solvable, they cannot be perfect. 相似文献
17.
A characterisation of finite soluble groups in which Sylow permutability is a transitive relation by means of subgroup embedding
properties enjoyed by all the subgroups is proved. The key point is an extension of a subnormality criterion due to Wielandt.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
18.
19.
XU Mingchun 《中国科学A辑(英文版)》2006,49(9)
In this paper the author has solved a problem of Abe and liyori for the finite simple groups 2F4(q) and 2F4(2)'. 相似文献
20.
李碧荣 《纯粹数学与应用数学》2004,20(3):259-262,267
设G是有限群,p是|G|的一个素因子,P是G的一个Sylow p-子群.若下列条件之一满足,则G是p-幂零:(1)P的极大子群均在G中S-半正规且(|G|,p-1)=1;(2)P的二次极大子群均在G中S-半正规且(|G|,p2-1)=1. 相似文献