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Schur indices of perfect groups
Author(s):
Alexandre
Turull
Journal:
Proc. Amer. Math. Soc.
130
(2002),
367-370.
MSC (2000):
Primary 20C15
Posted:
June 8, 2001
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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  . 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:
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
Posted:
June 8, 2001
Additional Notes:
The author was partially supported by a grant from the NSA
Communicated by:
Stephen D. Smith
Copyright of article:
Copyright
2001,
American Mathematical Society
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