# How does Diagonal Subgroup Embedding Determine the Structure of a Group?

Research paper by Shouhong Qiao, Guohua Qian; Yanming Wang

Indexed on: 22 Dec '16Published on: 05 Dec '16Published in: Communications in Mathematics and Statistics

#### Abstract

Let G be a finite group. Let $$D =\{(g, g) g\in G\}$$ , the main diagonal subgroup of $$G\times G$$ . In this paper, we consider the suitable generalized normalities or index of D in $$G\times G$$ , some interesting results are obtained. Let G be a finite group. Let $$D =\{(g, g) g\in G\}$$ , the main diagonal subgroup of $$G\times G$$ . In this paper, we consider the suitable generalized normalities or index of D in $$G\times G$$ , some interesting results are obtained.G $$D =\{(g, g) g\in G\}$$ $$D =\{(g, g) g\in G\}$$ $$G\times G$$ $$G\times G$$D $$G\times G$$ $$G\times G$$