Let be a finite group and denote the set of complex irreducible character degrees of . In this paper, we prove that if is a finite group and is an almost simple group whose socle is a Mathieu group such that , then there exists an abelian subgroup of such that is isomorphic to . In view of Huppert's conjecture (2000), we also provide some examples to show that is not necessarily a direct product of and , and hence we cannot extend this conjecture to almost simple groups.
Cite this article
Seyed Hassan Alavi, Ashraf Daneshkhah, Ali Jafari, On groups with the same character degrees as almost simple groups with socle Mathieu groups. Rend. Sem. Mat. Univ. Padova 138 (2017), pp. 115–127DOI 10.4171/RSMUP/138-6