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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Simple groups, permutation groups, and probability
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by Martin W. Liebeck and Aner Shalev PDF
J. Amer. Math. Soc. 12 (1999), 497-520 Request permission


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:
  • Aner Shalev
  • Affiliation: Institute of Mathematics, Hebrew University, Jerusalem 91904, Israel
  • MR Author ID: 228986
  • ORCID: 0000-0001-9428-2958
  • Email:
  • 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 1999 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 12 (1999), 497-520
  • MSC (1991): Primary 20D06; Secondary 20P05
  • DOI:
  • MathSciNet review: 1639620