Simple groups, permutation groups,

and probability

Authors:
Martin W. Liebeck and Aner Shalev

Journal:
J. Amer. Math. Soc. **12** (1999), 497-520

MSC (1991):
Primary 20D06; Secondary 20P05

DOI:
https://doi.org/10.1090/S0894-0347-99-00288-X

MathSciNet review:
1639620

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0894-0347-99-00288-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.

Article copyright:
© Copyright 1999
American Mathematical Society