{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:TI4SZETK3KD6PM2FH2CYK45PY4","short_pith_number":"pith:TI4SZETK","schema_version":"1.0","canonical_sha256":"9a392c926ada87e7b3453e858573afc70607891dda6af769794cc2921cbcebac","source":{"kind":"arxiv","id":"1907.02396","version":1},"attestation_state":"computed","paper":{"title":"Exponent of a finite group admitting a coprime automorphism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Pavel Shumyatsky, Sara Rodrigues","submitted_at":"2019-07-04T13:34:00Z","abstract_excerpt":"Let $G$ be a finite group admitting a coprime automorphism $\\phi$ of order $n$. Denote by $G_{\\phi}$ the centralizer of $\\phi$ in $G$ and by $G_{-\\phi}$ the set $\\{ x^{-1}x^{\\phi}; \\ x\\in G\\}$. We prove the following results.\n  1. If every element from $G_{\\phi}\\cup G_{-\\phi}$ is contained in a $\\phi$-invariant subgroup of exponent dividing $e$, then the exponent of $G$ is $(e,n)$-bounded.\n  2. Suppose that $G_{\\phi}$ is nilpotent of class $c$. If $x^{e}=1$ for each $x \\in G_{-\\phi}$ and any two elements of $G_{-\\phi}$ are contained in a $\\phi$-invariant soluble subgroup of derived length $d$,"},"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":"1907.02396","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-07-04T13:34:00Z","cross_cats_sorted":[],"title_canon_sha256":"e56b2bd99460964478ca82690d7cbd9e7ef4cb745d70e5d302351761740d85da","abstract_canon_sha256":"4b45a4882742d7acf1a145148e8768e1923cfccf8b9f979a8d3a89e21f2a904f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:28.714063Z","signature_b64":"IyIHCyJEy0Z94INF1K4wUi6xpRhfc7k5gbD91QFDlpBafPmr4oIzKj36mMdn+BKCXxb2ZTwocPfhwmvcPYYHCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a392c926ada87e7b3453e858573afc70607891dda6af769794cc2921cbcebac","last_reissued_at":"2026-05-17T23:41:28.713220Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:28.713220Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exponent of a finite group admitting a coprime automorphism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Pavel Shumyatsky, Sara Rodrigues","submitted_at":"2019-07-04T13:34:00Z","abstract_excerpt":"Let $G$ be a finite group admitting a coprime automorphism $\\phi$ of order $n$. Denote by $G_{\\phi}$ the centralizer of $\\phi$ in $G$ and by $G_{-\\phi}$ the set $\\{ x^{-1}x^{\\phi}; \\ x\\in G\\}$. We prove the following results.\n  1. If every element from $G_{\\phi}\\cup G_{-\\phi}$ is contained in a $\\phi$-invariant subgroup of exponent dividing $e$, then the exponent of $G$ is $(e,n)$-bounded.\n  2. Suppose that $G_{\\phi}$ is nilpotent of class $c$. If $x^{e}=1$ for each $x \\in G_{-\\phi}$ and any two elements of $G_{-\\phi}$ are contained in a $\\phi$-invariant soluble subgroup of derived length $d$,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.02396","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":"1907.02396","created_at":"2026-05-17T23:41:28.713363+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.02396v1","created_at":"2026-05-17T23:41:28.713363+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.02396","created_at":"2026-05-17T23:41:28.713363+00:00"},{"alias_kind":"pith_short_12","alias_value":"TI4SZETK3KD6","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_16","alias_value":"TI4SZETK3KD6PM2F","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_8","alias_value":"TI4SZETK","created_at":"2026-05-18T12:33:27.125529+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/TI4SZETK3KD6PM2FH2CYK45PY4","json":"https://pith.science/pith/TI4SZETK3KD6PM2FH2CYK45PY4.json","graph_json":"https://pith.science/api/pith-number/TI4SZETK3KD6PM2FH2CYK45PY4/graph.json","events_json":"https://pith.science/api/pith-number/TI4SZETK3KD6PM2FH2CYK45PY4/events.json","paper":"https://pith.science/paper/TI4SZETK"},"agent_actions":{"view_html":"https://pith.science/pith/TI4SZETK3KD6PM2FH2CYK45PY4","download_json":"https://pith.science/pith/TI4SZETK3KD6PM2FH2CYK45PY4.json","view_paper":"https://pith.science/paper/TI4SZETK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.02396&json=true","fetch_graph":"https://pith.science/api/pith-number/TI4SZETK3KD6PM2FH2CYK45PY4/graph.json","fetch_events":"https://pith.science/api/pith-number/TI4SZETK3KD6PM2FH2CYK45PY4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TI4SZETK3KD6PM2FH2CYK45PY4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TI4SZETK3KD6PM2FH2CYK45PY4/action/storage_attestation","attest_author":"https://pith.science/pith/TI4SZETK3KD6PM2FH2CYK45PY4/action/author_attestation","sign_citation":"https://pith.science/pith/TI4SZETK3KD6PM2FH2CYK45PY4/action/citation_signature","submit_replication":"https://pith.science/pith/TI4SZETK3KD6PM2FH2CYK45PY4/action/replication_record"}},"created_at":"2026-05-17T23:41:28.713363+00:00","updated_at":"2026-05-17T23:41:28.713363+00:00"}