Schur indices of perfect groups
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- by Alexandre Turull PDF
- Proc. Amer. Math. Soc. 130 (2002), 367-370 Request permission
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 $n$.References
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Additional Information
- Alexandre Turull
- Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32611
- Email: turull@math.ufl.edu
- 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
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 367-370
- MSC (2000): Primary 20C15
- DOI: https://doi.org/10.1090/S0002-9939-01-06072-5
- MathSciNet review: 1862114