\title[Conjugacy classes of cyclic subgroups]{Counting conjugacy classes of cyclic subgroups for fusion systems}

\author{Sejong Park}
\address{Section de math\'ematiques, \'Ecole Polythechnique F\'ed\'erale de Lausanne, Station 8, CH-1015 Lausanne, Switzerland}

\date{July 2013}

\begin{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}.
\end{abstract}