A characterization of saturated fusion systems over abelian 2-groups

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  • Ellen Henke
Given a saturated fusion system FF over a 2-group S, we prove that S is abelian provided any element of 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
JournalAdvances in Mathematics
Volume127
Pages (from-to)1-5
ISSN0001-8708
DOIs
Publication statusPublished - 2014

ID: 137755021