Saved in:
Bibliographic Details
Main Authors: Glauberman, George, Lynd, Justin
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2602.01197
Tags: Add Tag
No Tags, Be the first to tag this record!
Table of Contents:
  • Suppose $p$ is a prime and $S$ is a Sylow $p$-subgroup of a finite group $G$. If $S$ is normal in $G$, then $Z(S)$ is the direct product of $S \cap Z(G)$ with $[Z(S), G]$. We prove an analogous result for all groups except in some cases where $p=2$ and $G$ is not solvable, where we have counterexamples. We also extend this result to fusion systems.