On groups with the same character degrees as almost simple groups with socle sporadic simple groups
Group Theory
2016-03-01 v2
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 a sporadic simple group H0 such that cd(G) = cd(H), then G' = H0 and 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.
Cite
@article{arxiv.1601.06380,
title = {On groups with the same character degrees as almost simple groups with socle sporadic simple groups},
author = {Seyed Hassan Alavi and Ashraf Daneshkhah and Ali Jafari},
journal= {arXiv preprint arXiv:1601.06380},
year = {2016}
}
Comments
11 pages. arXiv admin note: substantial text overlap with arXiv:1511.04129