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

 

Elements of specified order in simple algebraic groups


Author: R. Lawther
Journal: Trans. Amer. Math. Soc. 357 (2005), 221-245
MSC (2000): Primary 20G15
Published electronically: August 19, 2004
MathSciNet review: 2098093
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Abstract: In this paper we let $G$ be a simple algebraic group and $r$ be a natural number, and consider the codimension in $G$ of the variety of elements $g\in G$ satisfying $g^r=1$. We shall obtain a lower bound for this codimension which is independent of characteristic, and show that it is attained if $G$ is of adjoint type.


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Additional Information

R. Lawther
Affiliation: Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, United Kingdom
Address at time of publication: Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, Cambridge University, Cambridge CB3 0WB, United Kingdom

DOI: http://dx.doi.org/10.1090/S0002-9947-04-03694-3
PII: S 0002-9947(04)03694-3
Received by editor(s): July 18, 2003
Published electronically: August 19, 2004
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.