منابع مشابه
Probabilistic generation of finite simple groups, II
In earlier work it was shown that each nonabelian finite simple group G has a conjugacy class C such that, whenever 1 = x ∈G, the probability is greater than 1/10 that G= 〈x, y〉 for a random y ∈ C. Much stronger asymptotic results were also proved. Here we show that, allowing equality, the bound 1/10 can be replaced by 13/42; and, excluding an explicitly listed set of simple groups, the bound 2...
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let us consider the set of non-abelian finite simple groups which admit non-trivial irreducible projective representations of degree $le 7$ over an algebraically closed field $f$ of characteristic $pgeq 0$. we survey some recent results which lead to the complete list of the groups in this set which are $(2, 3, 7)$-generated and of those which are $(2,3)$-generated.
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let us consider the set of non-abelian finite simple groups which admit non-trivial irreducible projective representations of degree $le 7$ over an algebraically closed field $mathbb{f}$ of characteristic $pgeq 0$. we survey some recent results which lead to the complete list of the groups in this set which are $(2,3,7)$-generated and of those which are $(2,3)$-generated.
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Let G be a finite group and let d(G) be the minimal number of generators for G. It is well known that d(G) = 2 for all (non-abelian) finite simple groups. We prove that d(H) ≤ 4 for any maximal subgroup H of a finite simple group, and that this bound is best possible. We also investigate the random generation of maximal subgroups of simple and almost simple groups. By applying a recent theorem ...
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Suppose G is a group of order p^2q^2 where p>q are prime numbers and suppose P and Q are Sylow p-subgroups and Sylow q-subgroups of G, respectively. In this paper, we show that up to isomorphism, there are four groups of order p^2q^2 when Q and P are cyclic, three groups when Q is a cyclic and P is an elementary ablian group, p^2+3p/2+7 groups when Q is an elementary ablian group an...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1999
ISSN: 0021-8693
DOI: 10.1006/jabr.1999.7869