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

Alavi, Seyed Hassan; Daneshkah, Ashraf; Jafari, Ali

doi:10.4171/RSMUP/138-6

Alavi, Seyed Hassan ¹ ; Daneshkah, Ashraf ¹ ; Jafari, Ali ¹

¹ Bu-Ali Sina University, Hamedan, Iran

Rendiconti del Seminario Matematico della Università di Padova, Tome 138 (2017), pp. 115-127.

Résumé

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 : 2017-12-22

MR Zbl

DOI : 10.4171/RSMUP/138-6

Classification : 20
Mots-clés : Character degrees, almost simple groups, sporadic simple groups, Mathieu simple groups, Huppert’s conjecture

Affiliations des auteurs :

Alavi, Seyed Hassan ¹ ; Daneshkah, Ashraf ¹ ; Jafari, Ali ¹

¹ Bu-Ali Sina University, Hamedan, Iran

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     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 = {https://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. https://www.numdam.org/articles/10.4171/RSMUP/138-6/

Bibliographie
Cité par

Alavi, Seyed Hassan On groups with the same character degrees as almost simple groups with socle small Ree groups, Communications in Algebra, Volume 51 (2023) no. 10, p. 4372 | DOI:10.1080/00927872.2023.2209661
Madady Moghadam, Safoura; Iranmanesh, Ali Characterization of some almost simple groups with socle PSp4(q) by their character degrees, Journal of Algebra and Its Applications, Volume 22 (2023) no. 08 | DOI:10.1142/s0219498823501670
Alavi, Seyed Hassan; Daneshkhah, Ashraf; Zafarabad, Yazdan Momeni Groups with the same character degrees as almost simple Suzuki groups, Journal of Algebra and Its Applications, Volume 22 (2023) no. 09 | DOI:10.1142/s021949882350192x
Shirjian, Farrokh; Iranmanesh, Ali Extending Huppert’s conjecture to almost simple groups of Lie type, Illinois Journal of Mathematics, Volume 64 (2020) no. 1 | DOI:10.1215/00192082-8165590

Cité par 4 documents. Sources : Crossref