Fusion systems on small 𝑝-groups

Craven, David; Glesser, Adam

doi:10.1090/S0002-9947-2012-05580-2

Fusion systems on small $p$-groups
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by David A. Craven and Adam Glesser PDF

Trans. Amer. Math. Soc. 364 (2012), 5945-5967 Request permission

Abstract:

In this article we study several classes of ‘small’ $2$-groups: we complete the classification, started by Stancu, of all saturated fusion systems on metacyclic $p$-groups for all primes $p$. We consider Suzuki $2$-groups, and classify all center-free saturated fusion systems on $2$-groups of $2$-rank $2$. We end by classifying all possible $\mathcal {F}$-centric, $\mathcal {F}$-radical subgroups in saturated fusion systems on $2$-groups of $2$-rank $2$.

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