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Intersections of conjugacy classes and subgroups of algebraic groups

Author: Robert M. Guralnick
Journal: Proc. Amer. Math. Soc. 135 (2007), 689-693
MSC (2000): Primary 20G15
Published electronically: September 11, 2006
MathSciNet review: 2262864
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Abstract: We show that if $ H$ is a reductive group, then $ n$th roots of conjugacy classes are a finite union of conjugacy classes, and that if $ G$ is an algebraic overgroup of $ H$, then the intersection of $ H$ with a conjugacy class of $ G$ is a finite union of $ H$-conjugacy classes. These results follow from results on finiteness of unipotent classes in an almost simple algebraic group.

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Robert M. Guralnick
Affiliation: Department of Mathematics, University of Southern California, Los Angeles, California 90089-2532

Keywords: Conjugacy classes, algebraic groups, reductive groups, $n$th roots
Received by editor(s): October 11, 2005
Published electronically: September 11, 2006
Additional Notes: The author gratefully acknowledges the support of NSF grant DMS 0140578. He also thanks Ben Martin, Gerhard Röhrle and Daniel Goldstein for helpful comments, and the IAS for its support.
Communicated by: Lance W. Small
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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