{"paper":{"title":"A characterization of saturated fusion systems over abelian 2-groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Ellen Henke","submitted_at":"2013-05-17T17:39:24Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.4139","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}