On groups with the same character degrees as almost simple groups with socle Mathieu groups
Rendiconti del Seminario Matematico della Università di Padova, Tome 138 (2017), pp. 115-127.

Let G be a finite group and cd (G) denote the set of complex irreducible character degrees of G. In this paper, we prove that if G is a finite group and H is an almost simple group whose socle is a Mathieu group such that cd (G)= 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.

Publié le :
DOI : 10.4171/RSMUP/138-6
Classification : 20
Mots clés : Character degrees, almost simple groups, sporadic simple groups, Mathieu simple groups, Huppert’s conjecture
Alavi, Seyed Hassan 1 ; Daneshkah, Ashraf 1 ; Jafari, Ali 1

1 Bu-Ali Sina University, Hamedan, Iran
@article{RSMUP_2017__138__115_0,
     author = {Alavi, Seyed Hassan and Daneshkah, Ashraf and Jafari, Ali},
     title = {On groups with the same character degrees as almost simple groups with socle {Mathieu} groups},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {115--127},
     publisher = {European Mathematical Society Publishing House},
     address = {Zuerich, Switzerland},
     volume = {138},
     year = {2017},
     doi = {10.4171/RSMUP/138-6},
     mrnumber = {3743248},
     zbl = {1380.20007},
     url = {http://www.numdam.org/articles/10.4171/RSMUP/138-6/}
}
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Alavi, Seyed Hassan; Daneshkah, Ashraf; Jafari, Ali. On groups with the same character degrees as almost simple groups with socle Mathieu groups. Rendiconti del Seminario Matematico della Università di Padova, Tome 138 (2017), pp. 115-127. doi : 10.4171/RSMUP/138-6. http://www.numdam.org/articles/10.4171/RSMUP/138-6/

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