Variations on Glauberman's ZJ Theorem

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 $Z{J}_r(S)$ and $Z{J}_o(S)$ respectively and are often strictly larger.

minor adjustments