A topological interpretation about $m_{G,N}$ for finite group $G$ with normal subgroup $N$

Abstract

Let $G$ be a finite group and $N⊴G$. In this note, we construct a class poset of $G$ for some cyclic subgroup $C$ of $G$. And we find a relation between $m_{G,N}$ and the Euler characteristic of some nerve spaces of these posets(see Main Theorem).

In arXiv:1701.08018, we computed $m_{G,N}$ in special case when $|G:N|=p$ for some prime number. In this paper, we compute $m_{G,N}$ in general case. This paper has 11 pages. Welcome the comments