### 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

*Proceedings of the American Mathematical Society*,

*131*(1), 35-40. https://doi.org/10.1090/S0002-9939-02-06506-1

**A block theoretic analogue of a theorem of Glauberman and Thompson.** / Kessar, Radha; Linckelmann, Markus.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 131, no. 1, pp. 35-40. https://doi.org/10.1090/S0002-9939-02-06506-1

}

TY - JOUR

T1 - A block theoretic analogue of a theorem of Glauberman and Thompson

AU - Kessar, Radha

AU - Linckelmann, Markus

PY - 2003

Y1 - 2003

N2 - 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.

AB - 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.

U2 - 10.1090/S0002-9939-02-06506-1

DO - 10.1090/S0002-9939-02-06506-1

M3 - Article

VL - 131

SP - 35

EP - 40

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 1

ER -