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On the Glauberman and Watanabe correspondences for blocks of finite |
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| Authors: | M. E. Harris M. Linckelmann |
| Affiliation: | University of Minnesota, School of Mathematics, 105 Vincent Hall, Church Street SE, Minneapolis, Minnesota 55455-0487 M. Linckelmann ; CNRS, Université Paris 7, UFR Mathématiques, 2, place Jussieu, 75251 Paris Cedex 05, France |
| Abstract: | If  is a finite  -solvable group for some prime  ,  a solvable subgroup of the automorphism group of  of order prime to  such that  stabilises a  -block  of  and acts trivially on a defect group  of  , then there is a Morita equivalence between the block  and its Watanabe correspondent  of  , given by a bimodule  with vertex  and an endo-permutation module as source, which on the character level induces the Glauberman correspondence (and which is an isotypy by Watanabe's results). |
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