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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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1703.01917","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-03-06T15:16:38Z","cross_cats_sorted":[],"title_canon_sha256":"17f4426d5e2fa2fdb6007dcd864f1ceb042f5dc64c337e5071dcdfba5482147e","abstract_canon_sha256":"c59677867c78e9c9c9b28378fd02f0175069cbe2fa1320e5fbd31c9393db04ec"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:23.993084Z","signature_b64":"HWd0PryZaWXaRGBLzJW/+ClFVmluoSIQmzyrQOweROr+7taUTFaiZpHj8hUdJUlMCJ45G0+zfa0lRQBNNquSBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4331482f8f0c939cee518c40f59492b4e79998e802bc16b3d34ded86f585054f","last_reissued_at":"2026-05-17T23:48:23.992519Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:23.992519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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