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Simple groups, permutation groups, and probability

Author(s): Martin W. Liebeck; Aner Shalev
Journal: J. Amer. Math. Soc. 12 (1999), 497-520.
MSC (1991): Primary 20D06; Secondary 20P05
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Abstract: 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.

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Additional Information:

Martin W. Liebeck
Affiliation: Department of Mathematics, Imperial College, London SW7 2BZ, England
Email: m.liebeck@ic.ac.uk

Aner Shalev
Affiliation: Institute of Mathematics, Hebrew University, Jerusalem 91904, Israel
Email: shalev@math.huji.il

DOI: 10.1090/S0894-0347-99-00288-X
PII: S 0894-0347(99)00288-X
Received by editor(s): May 14, 1998
Received by editor(s) in revised form: August 26, 1998
Additional Notes: The second author acknowledges the support of the Israel Science Foundation, administered by the Israeli Academy of Sciences and Humanities.
Copyright of article: Copyright 1999, American Mathematical Society

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