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On $p$-permutation equivalences: Between Rickard equivalences and isotypies

On $p$-permutation equivalences: Between Rickard equivalences and isotypies

Broué and Rickard defined in their landmark papers from 1990 and 1996 the notions of an isotypy and a splendid equivalence between $p$-blocks of finite groups. Here, we define a notion of equivalence, which we call a $p$-permutation equivalence, that implies an isotypy and is implied by a splendid equivalence. …