Schur indices of perfect groups

Author:
Alexandre Turull

Journal:
Proc. Amer. Math. Soc. **130** (2002), 367-370

MSC (2000):
Primary 20C15

DOI:
https://doi.org/10.1090/S0002-9939-01-06072-5

Published electronically:
June 8, 2001

MathSciNet review:
1862114

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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

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Additional Information

**Alexandre Turull**

Affiliation:
Department of Mathematics, University of Florida, Gainesville, Florida 32611

Email:
turull@math.ufl.edu

DOI:
https://doi.org/10.1090/S0002-9939-01-06072-5

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