City Research Online

Abstract

We give a reduction to quasisimple groups for Donovan’s conjecture for blocks with abelian defect groups defined 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.

Publication Type:	Article
Subjects:	Q Science > QA Mathematics
Departments:	School of Science & Technology > Mathematics
SWORD Depositor:	Symplectic Administrator

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