Splitting the center of a Sylow subgroup
Abstract
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.
Fields of Study & Subjects
Finite Group Theory Research
Advanced Algebra and Geometry
Advanced Topics in Algebra
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 1 February 2026
- Document type
- Preprint