Abstract
Let be a finite group and be the set of all irreducible complex character degrees of without multiplicities. The aim of this paper is to propose an extension of Huppert’s conjecture from non-Abelian simple groups to almost simple groups of Lie type. Indeed, we conjecture that if is an almost simple group of Lie type with , then there exists an Abelian normal subgroup of such that . It is furthermore shown that is not necessarily the direct product of and . In view of Huppert’s conjecture, we also show that the converse implication does not necessarily hold for almost simple groups. Finally, in support of this conjecture, we will confirm it for projective general linear and unitary groups of dimension 3.
Citation
Farrokh Shirjian. Ali Iranmanesh. "Extending Huppert’s conjecture to almost simple groups of Lie type." Illinois J. Math. 64 (1) 49 - 69, April 2020. https://doi.org/10.1215/00192082-8165590
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