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They form a ring containing multiplications, the so-called finitary endomorphisms and non-trivial instances.\n  We show that inertial invertible endomorphisms form a group, provided $A$ has finite torsion-free rank. In any case, the group $IAut(A)$ they generate is commutative modulo the group $FAut(A)$ of finitary automorphisms, which is known to be locally finite.\n  We deduce that $IAut(A)$ is locally-(center-by-finite).\n  Also we conside"},"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":"1310.4625","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-10-17T09:14:33Z","cross_cats_sorted":[],"title_canon_sha256":"b8577bd64f6af1af682ccf32787d02e669c5572d7cebb29231fcaeb3eb04462d","abstract_canon_sha256":"eb66114f888c87e63cf4a57db2614644a1f3d80c19763a083a7cb641ec611266"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:13.533290Z","signature_b64":"tyGeJUzj6O5Yo8FLIzE2KLkNxdb9TPfVadjf3GU8NXloKfeoFYC5uvYn1YhE0+1foV64in4tOjCHecHrAb9jDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bb81c1b9377d9a4bc90652fd60f968ac803696dc6c5081205db65bcffd7b5b7f","last_reissued_at":"2026-05-18T03:10:13.532804Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:13.532804Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Inertial endomorphisms of an abelian group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Silvana Rinauro, Ulderico Dardano","submitted_at":"2013-10-17T09:14:33Z","abstract_excerpt":"We describe inertial endomorphisms of an abelian group $A$, that is endomorphisms $\\varphi$ with the property $|(\\varphi(X)+X)/X|<\\infty$ for each $X\\le A$. They form a ring containing multiplications, the so-called finitary endomorphisms and non-trivial instances.\n  We show that inertial invertible endomorphisms form a group, provided $A$ has finite torsion-free rank. In any case, the group $IAut(A)$ they generate is commutative modulo the group $FAut(A)$ of finitary automorphisms, which is known to be locally finite.\n  We deduce that $IAut(A)$ is locally-(center-by-finite).\n  Also we conside"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4625","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":"1310.4625","created_at":"2026-05-18T03:10:13.532871+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.4625v1","created_at":"2026-05-18T03:10:13.532871+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.4625","created_at":"2026-05-18T03:10:13.532871+00:00"},{"alias_kind":"pith_short_12","alias_value":"XOA4DOJXPWNE","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_16","alias_value":"XOA4DOJXPWNEXSIG","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_8","alias_value":"XOA4DOJX","created_at":"2026-05-18T12:28:06.772260+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/XOA4DOJXPWNEXSIGKL6WB6LIVS","json":"https://pith.science/pith/XOA4DOJXPWNEXSIGKL6WB6LIVS.json","graph_json":"https://pith.science/api/pith-number/XOA4DOJXPWNEXSIGKL6WB6LIVS/graph.json","events_json":"https://pith.science/api/pith-number/XOA4DOJXPWNEXSIGKL6WB6LIVS/events.json","paper":"https://pith.science/paper/XOA4DOJX"},"agent_actions":{"view_html":"https://pith.science/pith/XOA4DOJXPWNEXSIGKL6WB6LIVS","download_json":"https://pith.science/pith/XOA4DOJXPWNEXSIGKL6WB6LIVS.json","view_paper":"https://pith.science/paper/XOA4DOJX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.4625&json=true","fetch_graph":"https://pith.science/api/pith-number/XOA4DOJXPWNEXSIGKL6WB6LIVS/graph.json","fetch_events":"https://pith.science/api/pith-number/XOA4DOJXPWNEXSIGKL6WB6LIVS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XOA4DOJXPWNEXSIGKL6WB6LIVS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XOA4DOJXPWNEXSIGKL6WB6LIVS/action/storage_attestation","attest_author":"https://pith.science/pith/XOA4DOJXPWNEXSIGKL6WB6LIVS/action/author_attestation","sign_citation":"https://pith.science/pith/XOA4DOJXPWNEXSIGKL6WB6LIVS/action/citation_signature","submit_replication":"https://pith.science/pith/XOA4DOJXPWNEXSIGKL6WB6LIVS/action/replication_record"}},"created_at":"2026-05-18T03:10:13.532871+00:00","updated_at":"2026-05-18T03:10:13.532871+00:00"}