Browsing by Subject "Fusion system"

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    On functorial equivalence classes of blocks of finite groups
    (Elsevier BV * North-Holland, 2024-12) Yılmaz, Deniz
    Let k be an algebraically closed field of characteristic p > 0 and let F be an algebraically closed field of characteristic 0. Recently, together with Bouc, we introduced the notion of functorial equivalences between blocks of finite groups and proved that given a p -group D , there is only a finite number of pairs ( G, b ) of a finite group G and a block b of kG with defect groups isomorphic to D , up to functorial equivalence over F. In this paper, we classify the functorial equivalence classes over F of blocks with cyclic defect groups and 2 -blocks of defects 2 and 3. In particular, we prove that for all these blocks, the functorial equivalence classes depend only on the fusion system of the block.