A characterization of saturated fusion systems over abelian 2-groups

2013/05/17 by Henke, Ellen
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1305.4139

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.

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