### 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 |
---|---|

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

*p*-solvable groups.

*Transactions of the American Mathematical Society*,

*354*(9), 3435-3453. https://doi.org/10.1090/S0002-9947-02-02990-2

**On the Glauberman and Watanabe correspondences for blocks of finite p-solvable groups.** / Harris, M. E.; Linckelmann, Markus.

Research output: Contribution to journal › Article

*p*-solvable groups'

*Transactions of the American Mathematical Society*, vol. 354, no. 9, pp. 3435-3453. https://doi.org/10.1090/S0002-9947-02-02990-2

*p*-solvable groups. Transactions of the American Mathematical Society. 2002;354(9):3435-3453. https://doi.org/10.1090/S0002-9947-02-02990-2

}

TY - JOUR

T1 - On the Glauberman and Watanabe correspondences for blocks of finite p-solvable groups

AU - Harris, M. E.

AU - Linckelmann, Markus

PY - 2002

Y1 - 2002

N2 - 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).

AB - 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).

KW - ENDO-PERMUTATION MODULES

KW - EQUIVALENCES

KW - EXTENSIONS

U2 - 10.1090/S0002-9947-02-02990-2

DO - 10.1090/S0002-9947-02-02990-2

M3 - Article

VL - 354

SP - 3435

EP - 3453

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 9

ER -