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Glauberman-Watanabe corresponding $p$-blocks of finite groups with normal defect groups are Morita equivalent

Author: Morton E. Harris
Journal: Trans. Amer. Math. Soc. 357 (2005), 309-335
MSC (2000): Primary 20C20
Published electronically: April 27, 2004
MathSciNet review: 2098097
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Abstract: Let $G$ be a finite group and let $A$ be a solvable finite group that acts on $G$ such that the orders of $G$ and $A$are relatively prime. Let $b$ be a $p$-block of $G$ with normal defect group $D$ such that $A$ stabilizes $b$ and $D\leq C_{G}(A)$. Then there is a Morita equivalence between the block $b$ and its Watanabe correspondent block $W(b)$ of $C_{G}(A)$ given by a bimodule $M$ with vertex $\Delta D$ and trivial source that on the character level induces the Glauberman correspondence (and which is an isotypy by a theorem of Watanabe).

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Additional Information

Morton E. Harris
Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455

Received by editor(s): October 9, 2002
Received by editor(s) in revised form: July 29, 2003
Published electronically: April 27, 2004
Article copyright: © Copyright 2004 American Mathematical Society

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