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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Bounds on the number and sizes of conjugacy classes in finite Chevalley groups with applications to derangements


Authors: Jason Fulman and Robert Guralnick
Journal: Trans. Amer. Math. Soc. 364 (2012), 3023-3070
MSC (2010): Primary 20G40, 20B15
Published electronically: February 7, 2012
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Abstract: We present explicit upper bounds for the number and size of conjugacy classes in finite Chevalley groups and their variations. These results have been used by many authors to study zeta functions associated to representations of finite simple groups, random walks on Chevalley groups, the final solution to the Ore conjecture about commutators in finite simple groups and other similar problems. In this paper, we solve a strong version of the Boston-Shalev conjecture on derangements in simple groups for most of the families of primitive permutation group representations of finite simple groups (the remaining cases are settled in two other papers of the authors and applications are given in a third).


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Additional Information

Jason Fulman
Affiliation: Department of Mathematics, University of Southern California, Los Angeles, California 90089-2532
Email: fulman@usc.edu

Robert Guralnick
Affiliation: Department of Mathematics, University of Southern California, Los Angeles, California 90089-2532
Email: guralnic@usc.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05427-4
PII: S 0002-9947(2012)05427-4
Keywords: Number of conjugacy classes, simple group, Chevalley groups, partition, derangements, generating function
Received by editor(s): October 16, 2009
Received by editor(s) in revised form: July 21, 2010
Published electronically: February 7, 2012
Additional Notes: The first author was partially supported by National Science Foundation grants DMS 0503901, DMS 0802082, and National Security Agency grants MDA904-03-1-004, H98230-08-1-0133.
The second author was partially supported by National Science Foundation grants DMS 0140578 and DMS 0653873
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.