Abstract
We give a reduction to quasisimple groups for Donovan's conjecture for blocks with abelian defect groups dened with respect to a suitable discrete valuation ring O. Consequences are that Donovan's conjecture holds for O-blocks with abelian defect groups for the prime two, and that, using recent work of Farrell and Kessar, for arbitrary primes Donovan's conjecture for O-blocks with abelian defect groups reduces to bounding the Cartan invariants of blocks of quasisimple groups in terms of the defect. A result of independent interest is that in general (i.e. for arbitrary defect groups) Donovan's conjecture for O-blocks is a consequence of conjectures predicting bounds on the O-Frobenius number and on the Cartan invariants, as was proved by Kessar for blocks defined over an algebraically closed field.
Original language | English |
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Pages (from-to) | 249-264 |
Number of pages | 16 |
Journal | Mathematische Zeitschrift |
Volume | 295 |
Early online date | 8 Jul 2019 |
DOIs | |
Publication status | Published - 2019 |