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

10.22108/ijgt.2021.126329.1659

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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