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
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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
MR Author ID:
113845
ORCID:
0000-0002-3284-9899
Email:
m.liebeck@ic.ac.uk
Aner Shalev
Affiliation:
Institute of Mathematics, Hebrew University, Jerusalem 91904, Israel
MR Author ID:
228986
ORCID:
0000-0001-9428-2958
Email:
shalev@math.huji.il
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