Elements of specified order in simple algebraic groups

Lawther, R.

doi:10.1090/S0002-9947-04-03694-3

Elements of specified order in simple algebraic groups
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Trans. Amer. Math. Soc. 357 (2005), 221-245 Request permission

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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