Fusion systems on $p$ -groups with an extraspecial subgroup of index $p$

Moragues Moncho, Raul (2019). Fusion systems on $p$ -groups with an extraspecial subgroup of index $p$ . University of Birmingham. Ph.D.

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Abstract

In this thesis we classify saturated fusion systems on $p$ -groups $S$ containing an extraspecial subgroup of index $p$ for an arbitrary odd prime $p$ . We prove that if $F$ is a saturated fusion system on $S$ with $O_p(F)$ = 1 then either $|S|\leq p^6$ or $S$ is isomorphic to a unique group of order $p^{p-1}$