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Rationality of blocks of quasi-simple finite groups

Farrell, N. and Kessar, R. ORCID: 0000-0002-1893-4237 (2019). Rationality of blocks of quasi-simple finite groups. Representation Theory, 23, pp. 325-349. doi: 10.1090/ert/530

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 4jDj2!, 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.

Publication Type: Article
Additional Information: Published in Representation Theory in 2019, published by the American Mathematical Society.
Subjects: Q Science > QA Mathematics
Departments: School of Mathematics, Computer Science & Engineering > Mathematics
URI: http://openaccess.city.ac.uk/id/eprint/21597
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