The influence of minimal subgroups on saturated fusion systems

doi:10.1285/i15900932v36suppl1p91

The influence of minimal subgroups on saturated fusion systems

S. Ning

Abstract

Let $\cal F$ be a saturated fusion system over a \py group $S$ . In this paper, we investigate the influence of the minimal subgroups in $\mathfrak{foc}(\mathcal{F})$ , the focal subgroup of $\cal F$ . Our main result is that if for each cyclic subgroup $P\leq \mathfrak{foc}(\mathcal{F})$ of order $p$ (of order $2$ and $4$ if $p=2$ ) and each $\varphi\in \sHom_{\cal F}(P,\mathfrak{foc}(\mathcal{F}))$ , $\varphi$ extends to an automorphism of $S$ , then $S$ is normal in $\cal F$ . We also give several applications of this result

DOI Code: 10.1285/i15900932v36suppl1p91

Keywords: saturated fusion system; focal subgroup; resistant group

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The influence of minimal subgroups on saturated fusion systems

Abstract