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Intersections of conjugacy classes and subgroups of algebraic groups
Author(s):
Robert
M.
Guralnick
Journal:
Proc. Amer. Math. Soc.
135
(2007),
689-693.
MSC (2000):
Primary 20G15
Posted:
September 11, 2006
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Abstract:
We show that if  is a reductive group, then  th roots of conjugacy classes are a finite union of conjugacy classes, and that if  is an algebraic overgroup of  , then the intersection of  with a conjugacy class of  is a finite union of  -conjugacy classes. These results follow from results on finiteness of unipotent classes in an almost simple algebraic group.
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Additional Information:
Robert
M.
Guralnick
Affiliation:
Department of Mathematics, University of Southern California, Los Angeles, California 90089-2532
Email:
guralnic@usc.edu
DOI:
10.1090/S0002-9939-06-08544-3
PII:
S 0002-9939(06)08544-3
Keywords:
Conjugacy classes,
algebraic groups,
reductive groups,
$n$th roots
Received by editor(s):
October 11, 2005
Posted:
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 of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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