A relation between $m_{G,N}$ and the Euler characteristic of the nerve space of some class poset of $G$

Heguo Liu, Xingzhong Xu, Jiping Zhang

Let $G$ be a finite group and $N⊴G$ with $|G:N|=p$ for some prime $p$. In this note, to compute $m_{G,N}$ directly, we construct a class poset ${\mathfrak{T}}_C(G)$ of $G$ f…