Abstract
Donovan’s conjecture states that there exist only finitely many Morita equivalence classes of p-blocks with a given defect. This conjecture was shown by Radha Kessar to be equivalent to two other conjectures, one of which is that the basic algebras of p-blocks with a given defect can all be defined over a single finite field. We shall show that this latter conjecture is equivalent to the seemingly stronger statement that all p-blocks with a given defect can be defined over a single finite field.
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Klupsch, M. Relating the Frobenius and Morita-Frobenius numbers of blocks of finite groups. Arch. Math. 108, 539–543 (2017). https://doi.org/10.1007/s00013-017-1042-3
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DOI: https://doi.org/10.1007/s00013-017-1042-3