A characterization of saturated fusion systems over abelian 2-groups
Research output: Contribution to journal › Journal article › Research › peer-review
Given a saturated fusion system FF 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 language | English |
---|---|
Journal | Advances in Mathematics |
Volume | 127 |
Pages (from-to) | 1-5 |
ISSN | 0001-8708 |
DOIs | |
Publication status | Published - 2014 |
ID: 137755021