Minimal Fusion Systems with a Unique Maximal Parabolic

Details Minimal Fusion Systems with a Unique Maximal Parabolic Minimal Fusion Systems with a Unique Maximal Parabolic

2010-07-13

arxiv.org/abs/1007.2159v3

Mathematics

Group Theory

To appear in the Journal of Algebra

Scientific paper

We define minimal fusion systems in a way that every non-solvable fusion system has a section which is minimal. Minimal fusion systems can also be seen as analogs of Thompson's N-groups. In this paper, we consider a minimal fusion system $\mathcal{F}$ on a finite $p$-group $S$ that has a unique maximal $p$-local subsystem containing $N_{\mathcal{F}}(S)$. For an arbitrary prime $p$, we determine the structure of a certain (explicitly described) $p$-local subsystem of $\mathcal{F}$. If $p=2$, this leads to a complete classification of the fusion system $\mathcal{F}$.

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