Counting conjugacy classes of cyclic subgroups for fusion systems

2013/07/09 by Sejong Park, Park, Sejong
Mathematics · #20C20 #Advanced Algebra and Geometry #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1307.2527

openalex publication_date 2013/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give another proof of an observation of Thévenaz \citeT1989 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 \citeP2010.

Related

• Realising fusion systems
• Realizing fusion systems inside finite groups
• Fusion systems on small p-groups
• Fusion invariant characters of p-groups
• Fusion systems over a Sylow p-subgroup of G₂(p)