Centralizers of normal subgroups and the Z*-theorem

E. Henke; J. Semeraro

doi:10.1016/j.jalgebra.2015.06.027

Centralizers of normal subgroups and the Z*-theorem

E. Henke, J. Semeraro

Mathematical Science

University of Bristol

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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Abstract

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.

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	https://doi.org/10.1016/j.jalgebra.2015.06.027
Publication status	Published - 1 Oct 2015

Keywords

finite groups
fusion systems
Glauberman's Z*-theorem

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NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Algebra. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Algebra, VOL 439 (2015) DOI: 10.1016/j.jalgebra.2015.06.027 This manuscript is distributed in accordance with the Creative Commons Attribution Non Commercial-No Derivs (CC BY-NC-ND 4.0) license, which permits others to distribute this work non-commercially provided the original work is properly cited and the use is non-commercial. See: http://creativecommons.org/licenses/by-nc-nd/4.0/
Accepted author manuscript, 262 KB

http://arxiv.org/abs/1411.1932

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KW - finite groups

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KW - Glauberman's Z-theorem

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JO - Journal of Algebra

JF - Journal of Algebra

ER -

Centralizers of normal subgroups and the Z*-theorem

Abstract

Keywords

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