Intersections of conjugacy classes and subgroups of algebraic groups
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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.References
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Additional Information
- Robert M. Guralnick
- Affiliation: Department of Mathematics, University of Southern California, Los Angeles, California 90089-2532
- MR Author ID: 78455
- Email: guralnic@usc.edu
- 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
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 689-693
- MSC (2000): Primary 20G15
- DOI: https://doi.org/10.1090/S0002-9939-06-08544-3
- MathSciNet review: 2262864