共查询到20条相似文献,搜索用时 15 毫秒
1.
It is proved that for finite groups G, the probability thattwo randomly chosen elements of G generate a soluble subgrouptends to zero as the index of the largest soluble normal subgroupof G tends to infinity. 相似文献
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We show that two random elements of a finite simple groupG generateG with probability 1 as |G| . This settles a conjecture of Dixon. 相似文献
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Nina E. Menezes Martyn Quick Colva M. Roney-Dougal 《Israel Journal of Mathematics》2013,198(1):371-392
We study the probability of generating a finite simple group, together with its generalisation P G,socG (d), the conditional probability of generating an almost simple finite group G by d elements, given that these elements generate G/socG. We prove that P G,socG (2) ? 53/90, with equality if and only if G is A6 or S6, and establish a similar result for P G,socG (3). Positive answers to longstanding questions of Wiegold on direct products, and of Mel’nikov on profinite groups, follow easily from our results. 相似文献
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In this paper generalized Fischer spaces are defined and some results on their classification are obtained. 相似文献
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We study the asymptotic behavior of the probability of generating a finite completely reducible linear group G of degree n with [ n] elements. In particular we prove that if 3/2 and n is large enough then [ n] randomly chosen elements that generate G modulo O2(G) almost certainly generate G itself.Received: 13 February 2003 相似文献
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We show that a countable totally and discretely ordered set with first element inherently carries the structure of an ordered commutative euclidean monoid, provided its order type is of a certain kind. As an application we specify the order types of all discretely ordered sets which can be expanded to ordered commutative euclidean monoids. 相似文献
10.
It is well known that a permutation group of degree
can be generated by
elements. In this paper we study
the asymptotic behavior of the probability of generating a
permutation group of degree n with
elements. In particular we prove that if n
is large enough and
elements generate a permutation group
G of degree
n
modulo G
G
2, then almost
certainly these elements generate G itself.
Received: 2 January 2002 相似文献
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We investigate groups in which every subgroup containing some fixed finite nilpotent subgroup has a complement. 相似文献
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Parama Dutta 《代数通讯》2018,46(3):961-969
Let G be a finite group and Aut(G) the automorphism group of G. The autocommuting probability of G, denoted by Pr(G,Aut(G)), is the probability that a randomly chosen automorphism of G fixes a randomly chosen element of G. In this paper, we study Pr(G,Aut(G)) through a generalization. We obtain a computing formula, several bounds and characterizations of G through Pr(G,Aut(G)). We conclude the paper by showing that the generalized autocommuting probability of G remains unchanged under autoisoclinism. 相似文献
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Miguel Torres 《Rendiconti del Circolo Matematico di Palermo》1993,42(3):362-368
Every finite group is generated by minimal sets of subnormal comonolithic subgroups all this sets having the same number of
members and whose perfect subgroups being the same for every such a set. The proof of this result depends on some well known
results about subnormal subgroups, mainly due to H. Wielandt. 相似文献
19.
Arie Bialostocki 《Israel Journal of Mathematics》1975,20(2):178-188
LetG be a finite group with an abelian Sylow 2-subgroup. LetA be a nilpotent subgroup ofG of maximal order satisfying class (A)≦k, wherek is a fixed integer larger than 1. Suppose thatA normalizes a nilpotent subgroupB ofG of odd order. ThenAB is nilpotent. Consequently, ifF(G) is of odd order andA is a nilpotent subgroup ofG of maximal order, thenF(G)?A. 相似文献