用非交换图刻画某些单群

Characterization of Some Simple Groups by Their Noncommuting Graphs

证明了:如果M是素图非连通的有限非交换单群,G是一个有限群,且(G)≌(M),则G≌M.

Let G be a non-abelian group and associate a non-commuting graph △↓（G） with G as follows, the vertex set of △↓（G）≌is G／Z（G） with two vertices x and y joined by an edge whenever the commutator of x and y is not the identity. In this short paper we prove that if M is a finite nonabelian simple group with disconnected prime graph, G is a finite group and △↓（G）≌△↓（M）, then G≌M.