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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Schur indices of perfect groups


Author: Alexandre Turull
Journal: Proc. Amer. Math. Soc. 130 (2002), 367-370
MSC (2000): Primary 20C15
Published electronically: June 8, 2001
MathSciNet review: 1862114
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Abstract:

It has been noticed by many authors that the Schur indices of the irreducible characters of many quasi-simple finite groups are at most $2$. A conjecture has emerged that the Schur indices of all irreducible characters of all quasi-simple finite groups are at most $2$. We prove that this conjecture cannot be extended to the set of all finite perfect groups. Indeed, we prove that, given any positive integer $n$, there exist irreducible characters of finite perfect groups of chief length $2$ which have Schur index $n$.


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Additional Information

Alexandre Turull
Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32611
Email: turull@math.ufl.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06072-5
PII: S 0002-9939(01)06072-5
Keywords: Brauer group, Schur index, linear groups, classical groups, characters, representations
Received by editor(s): June 23, 2000
Received by editor(s) in revised form: July 14, 2000
Published electronically: June 8, 2001
Additional Notes: The author was partially supported by a grant from the NSA
Communicated by: Stephen D. Smith
Article copyright: © Copyright 2001 American Mathematical Society



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