ON THOMPSON’S CONJECTURE FOR ALTERNATING GROUP \(A_26\) - Liu, Shitian; Huang, Yanhua (Italian Journal of Pure and Applied Mathematics, 2014)
Let G be a group. Denote by N(G) the set of nonidentity orders of conjugacy classes of elements in G. For groups A10, A16 and A22 which are uniquely determined by N(G), theses degrees are p+3 and p+4 is a prime with p = 7, 13, 19. If p+4 is composite, then whether can the groups Ap+3 be characterized by N(G). In this paper, we give an example for Ap+3 with p+4 composite, namely, we proved that if G is a group with trivial center and N(G) = N(A26), then G \(\) A26.