### 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 \G\ 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 DeltaP 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).

Original language | English |
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Pages (from-to) | 3435-3453 |

Number of pages | 18 |

Journal | Transactions of the American Mathematical Society |

Volume | 354 |

Issue number | 9 |

DOIs | |

Publication status | Published - 2002 |

### Keywords

- ENDO-PERMUTATION MODULES
- EQUIVALENCES
- EXTENSIONS

## Cite this

Harris, M. E., & Linckelmann, M. (2002). On the Glauberman and Watanabe correspondences for blocks of finite

*p*-solvable groups.*Transactions of the American Mathematical Society*,*354*(9), 3435-3453. https://doi.org/10.1090/S0002-9947-02-02990-2