### Abstract

Original language | English |
---|---|

Pages (from-to) | 511-514 |

Number of pages | 4 |

Journal | Journal of Algebra |

Volume | 439 |

Early online date | 16 Jul 2015 |

DOIs | |

Publication status | Published - 1 Oct 2015 |

### Fingerprint

### Keywords

- finite groups
- fusion systems
- Glauberman's Z*-theorem

### Cite this

*Journal of Algebra*,

*439*, 511-514. https://doi.org/10.1016/j.jalgebra.2015.06.027

**Centralizers of normal subgroups and the Z*-theorem.** / Henke, E.; Semeraro, J.

Research output: Contribution to journal › Article

*Journal of Algebra*, vol. 439, pp. 511-514. https://doi.org/10.1016/j.jalgebra.2015.06.027

}

TY - JOUR

T1 - Centralizers of normal subgroups and the Z*-theorem

AU - Henke, E.

AU - Semeraro, J.

PY - 2015/10/1

Y1 - 2015/10/1

N2 - Glauberman's Z*-theorem and analogous statements for odd primes show that, for any prime p and any finite group G with Sylow p-subgroup S , the centre of G/Op′(G)G/Op′(G) is determined by the fusion system FS(G)FS(G). Building on these results we show a statement that seems a priori more general: For any normal subgroup H of G with Op′(H)=1Op′(H)=1, the centralizer CS(H)CS(H) is expressed in terms of the fusion system FS(G)FS(G) and its normal subsystem induced by H.

AB - Glauberman's Z*-theorem and analogous statements for odd primes show that, for any prime p and any finite group G with Sylow p-subgroup S , the centre of G/Op′(G)G/Op′(G) is determined by the fusion system FS(G)FS(G). Building on these results we show a statement that seems a priori more general: For any normal subgroup H of G with Op′(H)=1Op′(H)=1, the centralizer CS(H)CS(H) is expressed in terms of the fusion system FS(G)FS(G) and its normal subsystem induced by H.

KW - finite groups

KW - fusion systems

KW - Glauberman's Z-theorem

U2 - 10.1016/j.jalgebra.2015.06.027

DO - 10.1016/j.jalgebra.2015.06.027

M3 - Article

VL - 439

SP - 511

EP - 514

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -