{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:3U7E32G7BGW6BQWMKOJXGNSAZJ","short_pith_number":"pith:3U7E32G7","schema_version":"1.0","canonical_sha256":"dd3e4de8df09ade0c2cc5393733640ca587aa4c85185e154a43019e1dd471ce1","source":{"kind":"arxiv","id":"1408.1821","version":2},"attestation_state":"computed","paper":{"title":"Palindromic words in simple groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Andreas Thom, Elisabeth Fink","submitted_at":"2014-08-08T11:19:26Z","abstract_excerpt":"A palindrome is a word that reads the same left-to-right as right-to-left. We show that every simple group has a finite generating set $X$, such that every element of it can be written as a palindrome in the letters of $X$. Moreover, every simple group has palindromic width $pw(G,X)=1$, where $X$ only differs by at most one Nielsen-transformation from any given generating set. On the contrary, we prove that all non-abelian finite simple groups $G$ also have a generating set $S$ with $pw(G,S)>1$.\n  As a by-product of our work we also obtain that every just-infinite group has finite palindromic "},"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":"1408.1821","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-08-08T11:19:26Z","cross_cats_sorted":[],"title_canon_sha256":"90881e40c89d2e7444b1458f34f0fec63c80c088219536c93f3c6d929ed908a6","abstract_canon_sha256":"2c4a1618389ba03bd477bdae09f48824e63b4b7b25c8c6383848e39ab7cf42d4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:11.236163Z","signature_b64":"aPLgXlk9tZTlvE1ljwiVS4UT7Zx4OiaPbK+wwG7X5D1vUVQJBLuf2Y5ftMJfVU3nBg1rW+W4AL1onfbbBBHyAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dd3e4de8df09ade0c2cc5393733640ca587aa4c85185e154a43019e1dd471ce1","last_reissued_at":"2026-05-18T02:31:11.235582Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:11.235582Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Palindromic words in simple groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Andreas Thom, Elisabeth Fink","submitted_at":"2014-08-08T11:19:26Z","abstract_excerpt":"A palindrome is a word that reads the same left-to-right as right-to-left. We show that every simple group has a finite generating set $X$, such that every element of it can be written as a palindrome in the letters of $X$. Moreover, every simple group has palindromic width $pw(G,X)=1$, where $X$ only differs by at most one Nielsen-transformation from any given generating set. On the contrary, we prove that all non-abelian finite simple groups $G$ also have a generating set $S$ with $pw(G,S)>1$.\n  As a by-product of our work we also obtain that every just-infinite group has finite palindromic "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.1821","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1408.1821","created_at":"2026-05-18T02:31:11.235685+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.1821v2","created_at":"2026-05-18T02:31:11.235685+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.1821","created_at":"2026-05-18T02:31:11.235685+00:00"},{"alias_kind":"pith_short_12","alias_value":"3U7E32G7BGW6","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_16","alias_value":"3U7E32G7BGW6BQWM","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_8","alias_value":"3U7E32G7","created_at":"2026-05-18T12:28:11.866339+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/3U7E32G7BGW6BQWMKOJXGNSAZJ","json":"https://pith.science/pith/3U7E32G7BGW6BQWMKOJXGNSAZJ.json","graph_json":"https://pith.science/api/pith-number/3U7E32G7BGW6BQWMKOJXGNSAZJ/graph.json","events_json":"https://pith.science/api/pith-number/3U7E32G7BGW6BQWMKOJXGNSAZJ/events.json","paper":"https://pith.science/paper/3U7E32G7"},"agent_actions":{"view_html":"https://pith.science/pith/3U7E32G7BGW6BQWMKOJXGNSAZJ","download_json":"https://pith.science/pith/3U7E32G7BGW6BQWMKOJXGNSAZJ.json","view_paper":"https://pith.science/paper/3U7E32G7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.1821&json=true","fetch_graph":"https://pith.science/api/pith-number/3U7E32G7BGW6BQWMKOJXGNSAZJ/graph.json","fetch_events":"https://pith.science/api/pith-number/3U7E32G7BGW6BQWMKOJXGNSAZJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3U7E32G7BGW6BQWMKOJXGNSAZJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3U7E32G7BGW6BQWMKOJXGNSAZJ/action/storage_attestation","attest_author":"https://pith.science/pith/3U7E32G7BGW6BQWMKOJXGNSAZJ/action/author_attestation","sign_citation":"https://pith.science/pith/3U7E32G7BGW6BQWMKOJXGNSAZJ/action/citation_signature","submit_replication":"https://pith.science/pith/3U7E32G7BGW6BQWMKOJXGNSAZJ/action/replication_record"}},"created_at":"2026-05-18T02:31:11.235685+00:00","updated_at":"2026-05-18T02:31:11.235685+00:00"}