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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.

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Authors and Affiliations

  1. Department of Mathematics, University of Southern Calfornia, 90089-1113, Los Angeles, CA, USA

    Robert M. Guralnick

  2. Department of Mathematics, University of Florida, 32611, Gainesville, FL, USA

    Geoffrey R. Robinson

Authors
  1. Robert M. Guralnick
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  2. Geoffrey R. Robinson
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Corresponding author

Correspondence to Robert M. Guralnick.

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For John Thompson

Partially supported by NSF grant DMS-91011407.

Partially supported by NSF grant DMS-9208667.

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Guralnick, R.M., Robinson, G.R. On extensions of the Baer-Suzuki Theorem. Israel J. Math. 82, 281–297 (1993). https://doi.org/10.1007/BF02808114

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  • DOI: https://doi.org/10.1007/BF02808114

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