A CHARACTERIZATION OF THE GROUP A22 BY NON-COMMUTING GRAPH

Title & Authors
A CHARACTERIZATION OF THE GROUP A22 BY NON-COMMUTING GRAPH

Abstract
Let G be a finite non-abelian group. We define the non-commuting graph $\small{{\nabla}(G)}$ of G as follows: the vertex set of $\small{{\nabla}(G)}$ is G-Z(G) and two vertices x and y are adjacent if and only if $\small{xy{\neq}yx}$. In this paper we prove that if G is a finite group with $\small{{\nabla}(G){\simeq_-}{\nabla}(\mathbb{A}_{22})}$, then $\small{G{\simeq_-}\mathbb{A}_{22}}$where $\small{\mathbb{A}_{22}}$ is the alternating group of degree 22.
Keywords
finite group;non-commuting graph;prime graph;alternating group;
Language
English
Cited by
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