A new characterization of A(10) by its noncommuting graph

作者：Wang Lingli; Shi Wujie^*

来源：Communications in Algebra, 2008, 36(2): 523-528.

DOI：10.1080/00927870701718906

• conjugacy class
• finite group
• noncommuting graph

Let G be a nonabelian group and associate a noncommuting graph V(G) with G as follows: The vertex set of V(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 1987, Professor J. G. Thompson gave the following conjecture.
Thompson's Conjecture. If G is a finite group with Z(G) = 1 and M is a nonabelian simple group satisfying N(G) = N(M), then G congruent to M, where N(G) := {n is an element of N I G has a conjugacy class of size n}.
In 2006, A. Abdollahi, S. Akbari, and H. R. Maimani put forward a conjecture (AAM's conjecture) in Abdollahi et al. (2006) as follows.
AAM's Conjecture. Let M be a finite nonabelian simple group and G a group such that del(G) congruent to del(M). Then G congruent to M. In this short article we prove that if G is a finite group with del(G) congruent to del(A(10)), then G congruent to A10, where A(10) is the alternating group of degree 10.

• 出版日期2008-2
• 单位宿州学院; 苏州大学