Authors: M R Darafsheh M Davoudi Monfared
Publish Date: 2011/05/20
Volume: 62, Issue: 11, Pages: 1673-1679
Abstract
Let G be a finite nonAbelian group We define a graph Γ G called the noncommuting graph of G with a vertex set G − ZG such that two vertices x and y are adjacent if and only if xy ≠ yx Abdollahi Akbari and Maimani put forward the following conjecture the AAM conjecture If S is a finite nonAbelian simple group and G is a group such that Γ S ≅ Γ G then S ≅ G It is still unknown if this conjecture holds for all simple finite groups with connected prime graph except mathbbA 10 L 48 L 44 and U 44 In this paper we prove that if mathbbA 16 denotes the alternating group of degree 16 then for any finite group G the graph isomorphism Gamma mathbbA 16 cong Gamma G implies that mathbbA 16 cong G
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