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ON HUPPERT’S CONJECTURE FOR THE CONWAY AND FISCHER FAMILIES OF SPORADIC SIMPLE GROUPS

Part of: Representation theory of groups

Published online by Cambridge University Press:  11 April 2013

S. H. ALAVI ,
A. DANESHKHAH ,
H. P. TONG-VIET  and
T. P. WAKEFIELD
S. H. ALAVI
Affiliation:
Department of Mathematics, Faculty of Science, Bu-Ali Sina University, Hamedan, Iran email alavi.s.hassan@gmail.comalavi.s.hassan@basu.ac.iradanesh@basu.ac.ir
A. DANESHKHAH*
Affiliation:
Department of Mathematics, Faculty of Science, Bu-Ali Sina University, Hamedan, Iran email alavi.s.hassan@gmail.comalavi.s.hassan@basu.ac.iradanesh@basu.ac.ir
H. P. TONG-VIET
Affiliation:
School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Pietermaritzburg 3209, South Africa email Tongviet@ukzn.ac.za
T. P. WAKEFIELD
Affiliation:
Department of Mathematics and Statistics, Youngstown State University, Youngstown, Ohio 44555, USA email tpwakefield@ysu.edu
*
✉daneshkhah.ashraf@gmail.com
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Abstract

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Let $G$ denote a finite group and $\mathrm{cd} (G)$ the set of irreducible character degrees of $G$. Huppert conjectured that if $H$ is a finite nonabelian simple group such that $\mathrm{cd} (G)= \mathrm{cd} (H)$, then $G\cong H\times A$, where $A$ is an abelian group. He verified the conjecture for many of the sporadic simple groups and we complete its verification for the remainder.

Keywords

character degreessporadic simple groupsHuppert’s conjecture

MSC classification

Secondary: 20C15: Ordinary representations and characters
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 94 , Issue 3 , June 2013 , pp. 289 - 303
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

References

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