{"paper":{"title":"Loewy lengths of centers of blocks II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Benjamin Sambale, Burkhard K\\\"ulshammer, Yoshihiro Otokita","submitted_at":"2017-03-06T15:16:38Z","abstract_excerpt":"Let ZB be the center of a p-block B of a finite group with defect group D. We show that the Loewy length LL(ZB) of ZB is bounded by $\\frac{|D|}{p}+p-1$ provided D is not cyclic. If D is non-abelian, we prove the stronger bound $LL(ZB)<\\min\\{p^{d-1},4p^{d-2}\\}$ where $|D|=p^d$. Conversely, we classify the blocks B with $LL(ZB)\\ge\\min\\{p^{d-1},4p^{d-2}\\}$. This extends some results previously obtained by the present authors. Moreover, we characterize blocks with uniserial center."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.01917","kind":"arxiv","version":1},"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"}