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- W2950298248 abstract "This article is dedicated to the proof of the following theorem. Let G be a finite group, p be a prime number, and e be a p-block of G. Assume that the centraliser C_G(P) of an e-subpair (P,e_P) strongly controls the fusion of the block e, and that a defect group of e is either abelian or (for odd p) has a non-cyclic center. Then there exists a stable equivalence of Morita type between the block algebras OGe and OC_G(P)e_P, where O is a complete discrete valuation ring of residual characteristic p. This stable equivalence is constructed by gluing together a family of local Morita equivalences, which are induced by bimodules with fusion-stable endo-permutation sources. Brou'e had previously obtained a similar result for principal blocks, in relation with the search for a modular proof of the odd Z*p-theorem. Thus our theorem points towards a block-theoretic analogue of the Z*p-theorem, which we state in terms of fusion control and Morita equivalences." @default.
- W2950298248 created "2019-06-27" @default.
- W2950298248 creator A5072473351 @default.
- W2950298248 date "2013-08-26" @default.
- W2950298248 modified "2023-09-26" @default.
- W2950298248 title "Strong fusion control and stable equivalences" @default.
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