Let G be a nite group and cd.G/ denote the set of complex irreducible character degrees of G. In this paper, we prove that if G is a nite group and H is an almost simple group whose socle is a Mathieu group such that cd.G/ D cd.H /, then there exists an abelian subgroup A of G such that G=A is isomorphic to H. In view of Huppert’s conjecture (2000), we also provide some examples to show that G is not necessarily a direct product of A and H , and hence we cannot extend this conjecture to almost simple groups.
