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RATIONALITY OF BLOCKS OF QUASI-SIMPLE FINITE GROUPS.
- Source :
- Representation Theory; 9/30/2019, Vol. 23, p325-349, 25p
- Publication Year :
- 2019
-
Abstract
- Let l be a prime number. We show that the Morita Frobenius number of an l-block of a quasi-simple finite group is at most 4 and that the strong Frobenius number is at most 4|D|²!, where D denotes a defect group of the block. We deduce that a basic algebra of any block of the group algebra of a quasi-simple finite group over an algebraically closed field of characteristic l is defined over a field with la elements for some a ≤ 4. We derive consequences for Donovan's conjecture. In particular, we show that Donovan's conjecture holds for l-blocks of special linear groups. [ABSTRACT FROM AUTHOR]
- Subjects :
- FINITE groups
GROUP algebras
PRIME numbers
ALGEBRA
FROBENIUS groups
Subjects
Details
- Language :
- English
- ISSN :
- 10884165
- Volume :
- 23
- Database :
- Complementary Index
- Journal :
- Representation Theory
- Publication Type :
- Academic Journal
- Accession number :
- 138971044
- Full Text :
- https://doi.org/10.1090/ert/530