## 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

## 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.## References

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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.
- © Copyright 1999 American Mathematical Society
- 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