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

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.

Keywords

Main diagonal subgroups / Abelian groups / Nilpotent groups / Supersoluble groups / Soluble groups

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Funding

National Natural Science Foundation of China(11201082)

National Natural Science Foundation of China(11471054)

Guangdong Science and Technology Department(Yq2013061)