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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 Science & Technology > Mathematics

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