{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:ZK4CWQMQEUYBEBPA5ACFIFAQAC","short_pith_number":"pith:ZK4CWQMQ","schema_version":"1.0","canonical_sha256":"cab82b419025301205e0e80454141000975cead04a64242299b0745d852f44c8","source":{"kind":"arxiv","id":"1807.08342","version":1},"attestation_state":"computed","paper":{"title":"On abelian group actions with TNI-centralizers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"G\\\"ulin Ercan, \\.Ismail \\c{S}. G\\\"ulo\\u{g}lu","submitted_at":"2018-07-22T18:43:08Z","abstract_excerpt":"A subgroup $H$ of a group $G$ is said to be a TNI-subgroup if $N_{G}(H)\\cap H^g=1$ for any $g\\in G\\,\\backslash \\,N_{G}(H).$ Let $A$ be an abelian group acting coprimely on the finite group $G$ by automorphisms in such a way that $C_G(A)=\\{g\\in G : g^a=g $\\, for all $a\\in A\\}$ is a solvable TNI-subgroup of $G$. We prove that $G$ is a solvable group with Fitting length $h(G)$ is at most $h(C_G(A))+\\ell(A)$. In particular $h(G)\\leq \\ell(A)+3$ whenever $C_G(A)$ is nonnormal. Here, $h(G)$ is the Fitting length of $G$ and $\\ell(A)$ is the number of primes dividing $A$ counted with multiplicities."},"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":"1807.08342","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-07-22T18:43:08Z","cross_cats_sorted":[],"title_canon_sha256":"6cebefec8bf6fa21b4458dae32ffaf18ad1a33e9c90f2f259851310248ba438a","abstract_canon_sha256":"293f3084441ef6705cd73f863cdda4a2c3a3474b7d8c05e244ac51f5f0e96c2f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:08.346943Z","signature_b64":"b5yKsQyMx+mco7NvwL/yvAR7UFAr7IxnIEn8hLfstXybjYOJserl8I1qNgswBXHFSSX0RNVBZArNeoQDmkGEAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cab82b419025301205e0e80454141000975cead04a64242299b0745d852f44c8","last_reissued_at":"2026-05-18T00:10:08.346267Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:08.346267Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On abelian group actions with TNI-centralizers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"G\\\"ulin Ercan, \\.Ismail \\c{S}. G\\\"ulo\\u{g}lu","submitted_at":"2018-07-22T18:43:08Z","abstract_excerpt":"A subgroup $H$ of a group $G$ is said to be a TNI-subgroup if $N_{G}(H)\\cap H^g=1$ for any $g\\in G\\,\\backslash \\,N_{G}(H).$ Let $A$ be an abelian group acting coprimely on the finite group $G$ by automorphisms in such a way that $C_G(A)=\\{g\\in G : g^a=g $\\, for all $a\\in A\\}$ is a solvable TNI-subgroup of $G$. We prove that $G$ is a solvable group with Fitting length $h(G)$ is at most $h(C_G(A))+\\ell(A)$. In particular $h(G)\\leq \\ell(A)+3$ whenever $C_G(A)$ is nonnormal. Here, $h(G)$ is the Fitting length of $G$ and $\\ell(A)$ is the number of primes dividing $A$ counted with multiplicities."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.08342","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":"1807.08342","created_at":"2026-05-18T00:10:08.346392+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.08342v1","created_at":"2026-05-18T00:10:08.346392+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.08342","created_at":"2026-05-18T00:10:08.346392+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZK4CWQMQEUYB","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZK4CWQMQEUYBEBPA","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZK4CWQMQ","created_at":"2026-05-18T12:33:07.085635+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/ZK4CWQMQEUYBEBPA5ACFIFAQAC","json":"https://pith.science/pith/ZK4CWQMQEUYBEBPA5ACFIFAQAC.json","graph_json":"https://pith.science/api/pith-number/ZK4CWQMQEUYBEBPA5ACFIFAQAC/graph.json","events_json":"https://pith.science/api/pith-number/ZK4CWQMQEUYBEBPA5ACFIFAQAC/events.json","paper":"https://pith.science/paper/ZK4CWQMQ"},"agent_actions":{"view_html":"https://pith.science/pith/ZK4CWQMQEUYBEBPA5ACFIFAQAC","download_json":"https://pith.science/pith/ZK4CWQMQEUYBEBPA5ACFIFAQAC.json","view_paper":"https://pith.science/paper/ZK4CWQMQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.08342&json=true","fetch_graph":"https://pith.science/api/pith-number/ZK4CWQMQEUYBEBPA5ACFIFAQAC/graph.json","fetch_events":"https://pith.science/api/pith-number/ZK4CWQMQEUYBEBPA5ACFIFAQAC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZK4CWQMQEUYBEBPA5ACFIFAQAC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZK4CWQMQEUYBEBPA5ACFIFAQAC/action/storage_attestation","attest_author":"https://pith.science/pith/ZK4CWQMQEUYBEBPA5ACFIFAQAC/action/author_attestation","sign_citation":"https://pith.science/pith/ZK4CWQMQEUYBEBPA5ACFIFAQAC/action/citation_signature","submit_replication":"https://pith.science/pith/ZK4CWQMQEUYBEBPA5ACFIFAQAC/action/replication_record"}},"created_at":"2026-05-18T00:10:08.346392+00:00","updated_at":"2026-05-18T00:10:08.346392+00:00"}