Mixing and generation in simple groups
نویسندگان
چکیده
منابع مشابه
finite simple groups of low rank: hurwitz generation and $(2,3)$-generation
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.
متن کاملfinite simple groups of low rank: hurwitz generation and (2,3)-generation
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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For each nite simple group G there is a conjugacy class C G such that each nontrivial element of G generates G together with any of more than 1/10 of the members of C G. Precise asymptotic results are obtained for the probability implicit in this assertion.
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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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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2008
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2007.07.031