A characterization of saturated fusion systems over abelian 2-groups

Ellen Henke

A characterization of saturated fusion systems over abelian 2-groups

Group Theory 2014-02-17 v2

Authors: Ellen Henke

Abstract

Given a saturated fusion system $\mathcal{F}$ over a $2$ -group $S$ , we prove that $S$ is abelian provided any element of $S$ is $\mathcal{F}$ -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.

Keywords

saturated fusion systems abelian 2-groups finite groups defect groups 2-blocks Camina-Herzog theorem stable center

Cite

@article{arxiv.1305.4139,
  title  = {A characterization of saturated fusion systems over abelian 2-groups},
  author = {Ellen Henke},
  journal= {arXiv preprint arXiv:1305.4139},
  year   = {2014}
}

Comments

4 pages. One corollary added in the updated version. Accepted to appear in Adv. Math

A characterization of saturated fusion systems over abelian 2-groups

Abstract

Keywords

Cite

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