Conjugacy classes and characters for extensions of finite groups

Xiang Tang; Hsian-hua Tseng

Conjugacy classes and characters for extensions of finite groups

Group Theory 2014-08-19 v1

Authors: Xiang Tang , Hsian-hua Tseng

Abstract

Let $H$ be an extension of a finite group $Q$ by a finite group $G$ . Inspired by the results of duality theorems for \'etale gerbes on orbifolds, we describe the number of conjugacy classes of $H$ that maps to the same conjugacy class of $Q$ . Furthermore, we prove a generalization of the orthogonality relation between characters of $G$ .

Keywords

finite groups group extensions conjugacy classes characters orthogonality relation étale gerbes

Cite

@article{arxiv.1310.6384,
  title  = {Conjugacy classes and characters for extensions of finite groups},
  author = {Xiang Tang and Hsian-hua Tseng},
  journal= {arXiv preprint arXiv:1310.6384},
  year   = {2014}
}

Comments

10 pages

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