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

Seyed Hassan Alavi; Ashraf Daneshkhah; Ali Jafari

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

Group Theory 2016-01-26 v3

Authors: Seyed Hassan Alavi , Ashraf Daneshkhah , Ali Jafari

Abstract

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 Mathieu group such that $cd(G) =cd(H)$ , then there exists an Abelian subgroup $A$ of $G$ such that $G/A$ is isomorphic to $H$ . This study is heading towards the study of an extension of Huppert's conjecture (2000) for almost simple groups.

Keywords

finite group theory character theory group theory

Cite

@article{arxiv.1511.04129,
  title  = {On groups with the same character degrees as almost simple groups with socle the Mathieu groups},
  author = {Seyed Hassan Alavi and Ashraf Daneshkhah and Ali Jafari},
  journal= {arXiv preprint arXiv:1511.04129},
  year   = {2016}
}

Comments

arXiv admin note: text overlap with arXiv:1108.0010 by other authors

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

Abstract

Keywords

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