李型单群U_3(q)的非交换图刻画(英文)

A New Characterization of the Simple Group of Lie Type U_3(q) by Its Non-commuting Graph

假设U3(q)是一李型单群,其中q=pn,p是素数,n是自然数.若(G)≌(U3(q)),则G≌U3(q).从而,对于李型单群U3(q),AAM猜想是成立的.

Let G be a non-abellan group and associate a non-commutlng graph Δ↓ （G） with G as follows： the vertex set of Δ↓ （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. Let U3 （q） be a simple group of Lie type, where n ∈ N, q=p＇, and p is a prime. Namely, if G is a group with Δ↓（G）≌ Δ↓（U3 （q））, then G ≌ U3 （q）.