Centralizers of normal subgroups and the Z*-theorem

E. Henke, J. Semeraro

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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 languageEnglish
Pages (from-to)511-514
Number of pages4
JournalJournal of Algebra
Volume439
Early online date16 Jul 2015
DOIs
Publication statusPublished - 1 Oct 2015

Keywords

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

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