Conjugacy classes of maximal cyclic subgroups and nilpotence class of $p$-groups

In this paper, we set $η(G)$ to be the number of conjugacy classes of maximal cyclic subgroups of $G$. We prove that if $G$ is a $p$-group of order $p^n$ and nilpotence class $l$, then $η(G)$ is bounded below by a linear function in $n/l$.

No reviews yet.

No comments yet.