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arXiv · 1307.2527

Counting conjugacy classes of cyclic subgroups for fusion systems

Sejong Park
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Abstract

We give another proof of an observation of Th\'evenaz \cite{T1989} and present a fusion system version of it. Namely, for a saturated fusion system $\CF$ on a finite $p$-group $S$, we show that the number of the $\CF$-conjugacy classes of cyclic subgroups of $S$ is equal to the rank of certain square matrices of numbers of orbits, coming from characteristic bisets, the characteristic idempotent and finite groups realizing the fusion system $\CF$ as in our previous work \cite{P2010}.

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Sejong Park. 2013-07-09. Counting conjugacy classes of cyclic subgroups for fusion systems. https://arxiv.org/abs/1307.2527

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