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A characterization of the group A22 by non-commuting graph
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Let G be a finite non-abelian group. We define the noncommuting graph ∇(G) of G as follows: the vertex set of ∇(G) is G−Z(G) and two vertices x and y are adjacent if and only if xy 6≠ yx. In this paper we prove that if G is a finite group with ∇(G) ≅ ∇(A22), then G = A22, where A22 is the alternating group of degree 22.
Abstract
Let G be a finite non-abelian group. We define the noncommuting graph ∇(G) of G as follows: the vertex set of ∇(G) is G−Z(G) and two vertices x and y are adjacent if and only if xy 6≠ yx. In this paper we prove that if G is a finite group with ∇(G) ≅ ∇(A22), then G = A22, where A22 is the alternating group of degree 22.
참고문헌 (9)
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- L.Wang, "Recognition of some simple groups by their noncommuting graph", Monatsh. Math, 160(2), pp.211~221 (2010)
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