Donovan’s conjecture, crossed products and algebraic group actions
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Donovan’s conjecture, on blocks of finite group algebras over an algebraically closed field of prime characteristicp, asserts that for any finitep-groupD, there are only finitely many Morita equivalence classes of blocks with defect groupD. The main result of this paper is a reduction theorem: It suffices to prove the conjecture for groups generated by conjugates ofD. A number of other finiteness results are proved along the way. The main tool is a result on actions of algebraic groups.
KeywordsEquivalence Class Normal Subgroup Finite Group Algebraic Group Defect Group
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