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On the Glauberman and Watanabe correspondences for blocks of finite $p$-solvable groups


Authors: M. E. Harris and M. Linckelmann
Journal: Trans. Amer. Math. Soc. 354 (2002), 3435-3453
MSC (2000): Primary 20C20
DOI: https://doi.org/10.1090/S0002-9947-02-02990-2
Published electronically: April 9, 2002
MathSciNet review: 1911507
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Abstract: If $G$ is a finite $p$-solvable group for some prime $p$, $A$ a solvable subgroup of the automorphism group of $G$ of order prime to $\vert G\vert $such that $A$ stabilises a $p$-block $b$ of $G$ and acts trivially on a defect group $P$ of $b$, then there is a Morita equivalence between the block $b$ and its Watanabe correspondent $w(b)$ of $C_{G}(A)$, given by a bimodule $M$ with vertex $\Delta P$ 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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Additional Information

M. E. Harris
Affiliation: University of Minnesota, School of Mathematics, 105 Vincent Hall, Church Street SE, Minneapolis, Minnesota 55455-0487

M. Linckelmann
Affiliation: CNRS, Université Paris 7, UFR Mathématiques, 2, place Jussieu, 75251 Paris Cedex 05, France

DOI: https://doi.org/10.1090/S0002-9947-02-02990-2
Received by editor(s): July 16, 2001
Published electronically: April 9, 2002
Article copyright: © Copyright 2002 American Mathematical Society

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