用非交换图刻画L3(q)

摘要

Let G be a non-abelian group and associate a non-commuting graph ▽(G) with G as follows:the vertex set of ▽(G) is GZ(G) with two vertices x and y joined by an edge whenever the commutator of x and y is not the identity.We prove that if G is a finite group with ▽(G)(≌)▽(M),where M=L3(q)(q=pn,n∈N,p is a prime),then G(≌)M.%令G是一个有限群,其非交换图▽(G)如下定义:顶点集合▽(G)是GZ(G),当两条边x与y的换位子不等于单位元时x与y相连.我们证明了如果G是一个有限群,且▽(G)(≌)▽(M),其中M=L3(q),q=pn,p是素数n∈N,则G(≌)M.