{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:5THR4JQICMFDLMJJYFOACINZ5K","short_pith_number":"pith:5THR4JQI","schema_version":"1.0","canonical_sha256":"eccf1e2608130a35b129c15c0121b9eab474ac91bef45a088299700f31d2e60f","source":{"kind":"arxiv","id":"1812.01698","version":1},"attestation_state":"computed","paper":{"title":"On free subgroups in division rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Jairo Goncalves, Jason P. Bell","submitted_at":"2018-12-04T21:27:41Z","abstract_excerpt":"Let $K$ be a field and let $\\sigma$ be an automorphism and let $\\delta$ be a $\\sigma$-derivation of $K$. Then we show that the multiplicative group of nonzero elements of the division ring $D=K(x;\\sigma,\\delta)$ contains a free non-cyclic subgroup unless $D$ is commutative, answering a special case of a conjecture of Lichtman. As an application, we show that division algebras formed by taking the Goldie ring of quotients of group algebras of torsion-free non-abelian solvable-by-finite groups always contain free non-cyclic subgroups."},"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":"1812.01698","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-12-04T21:27:41Z","cross_cats_sorted":[],"title_canon_sha256":"5586e67ececd859de1b6da354718859cc2d478f5f533c4337dfcc87296026f49","abstract_canon_sha256":"7758b7234a1d074b25daa9778ae7fbaa1e76a934a3c0c9dc6a3f201131143537"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:00.871932Z","signature_b64":"xjIrh8Q1jAz04Bsf7HjXss0NolIu+oHFdhAzJYl2i5YSJc7BtwWbxL4HLpumv75L0jwPxhWpUcAbTa53v1E8Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eccf1e2608130a35b129c15c0121b9eab474ac91bef45a088299700f31d2e60f","last_reissued_at":"2026-05-17T23:59:00.871490Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:00.871490Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On free subgroups in division rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Jairo Goncalves, Jason P. Bell","submitted_at":"2018-12-04T21:27:41Z","abstract_excerpt":"Let $K$ be a field and let $\\sigma$ be an automorphism and let $\\delta$ be a $\\sigma$-derivation of $K$. Then we show that the multiplicative group of nonzero elements of the division ring $D=K(x;\\sigma,\\delta)$ contains a free non-cyclic subgroup unless $D$ is commutative, answering a special case of a conjecture of Lichtman. As an application, we show that division algebras formed by taking the Goldie ring of quotients of group algebras of torsion-free non-abelian solvable-by-finite groups always contain free non-cyclic subgroups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.01698","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1812.01698","created_at":"2026-05-17T23:59:00.871573+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.01698v1","created_at":"2026-05-17T23:59:00.871573+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.01698","created_at":"2026-05-17T23:59:00.871573+00:00"},{"alias_kind":"pith_short_12","alias_value":"5THR4JQICMFD","created_at":"2026-05-18T12:32:08.215937+00:00"},{"alias_kind":"pith_short_16","alias_value":"5THR4JQICMFDLMJJ","created_at":"2026-05-18T12:32:08.215937+00:00"},{"alias_kind":"pith_short_8","alias_value":"5THR4JQI","created_at":"2026-05-18T12:32:08.215937+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5THR4JQICMFDLMJJYFOACINZ5K","json":"https://pith.science/pith/5THR4JQICMFDLMJJYFOACINZ5K.json","graph_json":"https://pith.science/api/pith-number/5THR4JQICMFDLMJJYFOACINZ5K/graph.json","events_json":"https://pith.science/api/pith-number/5THR4JQICMFDLMJJYFOACINZ5K/events.json","paper":"https://pith.science/paper/5THR4JQI"},"agent_actions":{"view_html":"https://pith.science/pith/5THR4JQICMFDLMJJYFOACINZ5K","download_json":"https://pith.science/pith/5THR4JQICMFDLMJJYFOACINZ5K.json","view_paper":"https://pith.science/paper/5THR4JQI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.01698&json=true","fetch_graph":"https://pith.science/api/pith-number/5THR4JQICMFDLMJJYFOACINZ5K/graph.json","fetch_events":"https://pith.science/api/pith-number/5THR4JQICMFDLMJJYFOACINZ5K/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5THR4JQICMFDLMJJYFOACINZ5K/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5THR4JQICMFDLMJJYFOACINZ5K/action/storage_attestation","attest_author":"https://pith.science/pith/5THR4JQICMFDLMJJYFOACINZ5K/action/author_attestation","sign_citation":"https://pith.science/pith/5THR4JQICMFDLMJJYFOACINZ5K/action/citation_signature","submit_replication":"https://pith.science/pith/5THR4JQICMFDLMJJYFOACINZ5K/action/replication_record"}},"created_at":"2026-05-17T23:59:00.871573+00:00","updated_at":"2026-05-17T23:59:00.871573+00:00"}