Elements of specified order in simple algebraic groups
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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.References
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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
- Received by editor(s): July 18, 2003
- Published electronically: August 19, 2004
- © Copyright 2004
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 357 (2005), 221-245
- MSC (2000): Primary 20G15
- DOI: https://doi.org/10.1090/S0002-9947-04-03694-3
- MathSciNet review: 2098093