Variations on Glauberman's ZJ theorem

Document Type : Research Paper

Author

Department of Mathematics, University of Texas at Austin, RLM 8.100, 2515 Speedway Stop C1200, Austin, Texas, USA 78712-1202

Abstract

We give a new proof of Glauberman's ZJ Theorem, in a form that clarifies the choices involved and offers more choices than classical treatments. In particular, we introduce two new ZJ-type subgroups of a $p$-group~$S$, that contain ZJr(S) and ZJo(S) respectively and can be strictly larger.

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References

[1] S. Gagola, Unpublished course notes, Year(s) unknown.
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[8] Stellmacher, B., An analogue to Glauberman’s ZJ-theorem, Proc. Amer. Math. Soc., 109 (1990) 925–929. Errata
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History

  • Receive Date: 04 December 2020
  • Revise Date: 12 April 2021
  • Accept Date: 13 April 2021
  • Published Online: 01 June 2022

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