Huppert's Conjecture for alternating groups

We prove that the alternating groups of degree at least 5 are uniquely determined up to an abelian direct factor by the set of degrees of their irreducible complex representations. This confirms Huppert's Conjecture for alternating groups. (C) 2016 Elsevier Inc. All rights reserved.National Research Foundation of South Africa [93408]; NSFC [11231008]SCI(E)ARTICLE353-37847