A characterization of saturated fusion systems over abelian 2-groups

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Abstract

Given a saturated fusion system F over a 2-group S, we prove that S is abelian provided any element of S is F-conjugate to an element of Z(S). This generalizes a Theorem of Camina--Herzog, leading to a significant simplification of its proof. More importantly, it follows that any 2-block B of a finite group has abelian defect groups if all B-subsections are major. Furthermore, every 2-block with a symmetric stable center has abelian defect groups.
Original languageEnglish
Pages (from-to)1-5
Number of pages5
JournalAdvances in Mathematics
Volume257
Early online date4 Mar 2014
DOIs
Publication statusPublished - 1 Jun 2014

Keywords

  • saturated fusion systems
  • modular representation theory
  • finite groups

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