### Abstract

If p is an odd prime, G a finite group and P a Sylow-p-subgroup of G, a theorem of Glauberman and Thompson states that G is p-nilpotent if and only if N-G (Z (J (P))) is p-nilpotent, where J (P) is the Thompson subgroup of P generated by all abelian subgroups of P of maximal order. Following a suggestion of G. R. Robinson, we prove a block-theoretic analogue of this theorem.

Original language | English |
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Pages (from-to) | 35-40 |

Number of pages | 5 |

Journal | Proceedings of the American Mathematical Society |

Volume | 131 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2003 |

## Cite this

Kessar, R., & Linckelmann, M. (2003). A block theoretic analogue of a theorem of Glauberman and Thompson.

*Proceedings of the American Mathematical Society*,*131*(1), 35-40. https://doi.org/10.1090/S0002-9939-02-06506-1