A characterization of saturated fusion systems over abelian 2-groups

Ellen Henke

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


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
Early online date4 Mar 2014
Publication statusPublished - 1 Jun 2014

Bibliographical note

Theorem 1 and Corollary 2 were conjectured by Külshammer, Navarro, Sambale and Tiep and answer the question posed in [5, Question 3.1] for p=2. The author would like to thank Benjamin Sambale for drawing her attention to this problem. Furthermore, she would like to thank an anonymous referee for suggesting Corollary 3.


  • saturated fusion systems
  • modular representation theory
  • finite groups


Dive into the research topics of 'A characterization of saturated fusion systems over abelian 2-groups'. Together they form a unique fingerprint.

Cite this