, Volume 82, Issue 1-3, pp 281-297

On extensions of the Baer-Suzuki Theorem

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Abstract

We find a necessary and sufficient condition for an element of prime order in a finite group to be in a normalp-subgroup. This generalizes the Baer-Suzuki Theorem. Our proof depends on a result about elements of prime order contained in a unique maximal subgroup containing a result of Wielandt. We discuss various consequences, linear and algebraic group versions of the result.

For John Thompson
Partially supported by NSF grant DMS-91011407.
Partially supported by NSF grant DMS-9208667.