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In a finite Bol loop of order relatively prime to 3, the commutant generates an abelian group of order dividing the order of the loop. This generalizes a well-known result for Moufang loops. After describing all extensions of a loop $K$ such that $K$ is in the left and middl"},"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":"math/0601363","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.GR","submitted_at":"2006-01-14T23:08:06Z","cross_cats_sorted":[],"title_canon_sha256":"aade396cf85c3196b5959345599254113efa7605a9e176de0a6f8c931ec90769","abstract_canon_sha256":"b852a2569ddf828bb8a12cf42166ab0f43361536b1a801564fc397c89224bcb6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:50.633050Z","signature_b64":"CZ06bP1d8KdxnLVNujuKzojITCLbILF0jPix8Xv6td+DSQLNBTDcnn0B0xSx6bGr80afHP/z8+IlFCf0IYINAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"265fa77b5c1d71d1b03c2403da112189124afd6cbcf89459f4387d2943d58d05","last_reissued_at":"2026-05-18T01:08:50.632572Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:50.632572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"When is the commutant of a Bol loop a subloop?","license":"","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"J.D. 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