Simple groups, permutation groups, and probability
Copyright policy )Simple groups, permutation groups, and probability
We derive a new bound for the minimal degree of an almost simple primitive permutation group, and settle a conjecture of Cameron and Kantor concerning the base size of such a group. Additional results concern random generation of simple groups, and the so-called genus conjecture of Guralnick and Thompson. Our proofs are based on probabilistic arguments, together with a new result concerning the size of the intersection of a maximal subgroup of a classical group with a conjugacy class of elements.
- Hebrew University of Jerusalem Israel
- Imperial College London United Kingdom
Coverings of curves, fundamental group, classical groups, generation of simple groups, simple groups, genus, almost simple groups, Primitive groups, base size, probabilistic group theory, Linear algebraic groups over finite fields, primitive permutation groups, Probabilistic methods in group theory, Simple groups: alternating groups and groups of Lie type, maximal subgroups, Arithmetic and combinatorial problems involving abstract finite groups
Coverings of curves, fundamental group, classical groups, generation of simple groups, simple groups, genus, almost simple groups, Primitive groups, base size, probabilistic group theory, Linear algebraic groups over finite fields, primitive permutation groups, Probabilistic methods in group theory, Simple groups: alternating groups and groups of Lie type, maximal subgroups, Arithmetic and combinatorial problems involving abstract finite groups
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