authors:
Silvia Onofrei and Radu Stancu
title:
A characteristic subgroup for fusion systems
abstract:
As a counterpart for the prime $2$ to Glauberman's $ZJ$-theorem, Stellmacher proves that any nontrivial $2$-group $S$ has a nontrivial characteristic subgroup $W(S)$ with the following property. For any finite $\Sigma_4$-free group $G$, with $S$ a Sylow $2$-subgroup of $G$ and with $O_2(G)$ self-centralizing, the subgroup $W(S)$ is normal in $G$. We generalize Stellmacher's result to fusion systems. A similar construction of $W(S)$ can be done for odd primes and gives rise to a Glauberman functor.
status:
submited to J of Algebra