title: On Thompson's conjecture for alternating groups A p+3.
abstract: Let G be a group. Denote by π(G) the set of prime divisors of |G|. Let GK(G) be the graph with vertex set π(G) such that two primes p and q in π(G) are joined by an edge if G has an element of order p · q. We set s(G) to denote the number of connected components of the prime graph GK(G). Denote by N(G) the set of nonidentity orders of conjugacy classes of elements in G. Alavi and Daneshkhah proved that the groups, A n where n = p, p + 1, p + 2 with s(G) ≥ 2, are characterized by N(G). As a development of these topics, we will prove that if G is a finite group with trivial center and N(G) = N(A p+3) with p + 2 composite, then G is isomorphic to A p+3.
authors.affiliation: School of Science, Sichuan University of Science and Engineering, Zigong, Sichuan 643000, China.
authors.forename: Shitian
authors.identifier: 0000-0003-0318-9235
authors.initials: S
authors.lastname: Liu
authors.affiliation: School of Science, Sichuan University of Science and Engineering, Zigong, Sichuan 643000, China.
authors.forename: Yong
authors.initials: Y
authors.lastname: Yang
mesh_terms: D000465:Algorithms; D008962:Models, Theoretical