JournalsrsmupVol. 138pp. 115–127

On groups with the same character degrees as almost simple groups with socle Mathieu groups

  • Seyed Hassan Alavi

    Bu-Ali Sina University, Hamedan, Iran
  • Ashraf Daneshkhah

    Bu-Ali Sina University, Hamedan, Iran
  • Ali Jafari

    Bu-Ali Sina University, Hamedan, Iran
On groups with the same character degrees as almost simple groups with socle Mathieu groups cover
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Abstract

Let GG be a finite group and cd(G)\mathrm {cd}(G) denote the set of complex irreducible character degrees of GG. In this paper, we prove that if GG is a finite group and HH is an almost simple group whose socle is a Mathieu group such that cd(G)=cd(H)\mathrm {cd}(G) =\mathrm {cd}(H), then there exists an abelian subgroup AA of GG such that G/AG/A is isomorphic to HH. In view of Huppert's conjecture (2000), we also provide some examples to show that GG is not necessarily a direct product of AA and HH, 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. 115–127

DOI 10.4171/RSMUP/138-6