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

Heguo Liu; Xingzhong Xu; Jiping Zhang

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

Group Theory 2018-03-06 v1

Authors: Heguo Liu , Xingzhong Xu , Jiping Zhang

Abstract

Let $G$ be a finite group and $N\unlhd G$ . 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).

Keywords

finite group normal subgroup class poset nerve space euler characteristic m_{G,N}

Cite

@article{arxiv.1803.01583,
  title  = {A topological interpretation about $m_{G, N}$ for finite group $G$ with normal subgroup $N$},
  author = {Heguo Liu and Xingzhong Xu and Jiping Zhang},
  journal= {arXiv preprint arXiv:1803.01583},
  year   = {2018}
}

Comments

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

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

Abstract

Keywords

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