Thévenaz [Arch. Math. (Basel) 52 (1989), no. 3, 209-211] made an interesting observation that the number of conjugacy classes of cyclic subgroups in a finite group G is equal to the rank of the matrix of the numbers of double cosets in G. We give another proof of this fact and present a fusion system version of it. In particular we use finite groups realizing the fusion system ℱ as in our previous work [Arch. Math. (Basel) 94 (2010), no. 5, 405-410]
展开▼
