Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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A CHARACTERIZATION OF THE GROUP A22 BY NON-COMMUTING GRAPH

  • Received : 2011.05.22
  • Published : 2013.01.31
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Abstract

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

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References

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