{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:MKDH74IVXI4ONUIXYE7DO4GCTC","short_pith_number":"pith:MKDH74IV","schema_version":"1.0","canonical_sha256":"62867ff115ba38e6d117c13e3770c298b710346901d6c29f218f7870ab7d905c","source":{"kind":"arxiv","id":"1106.0373","version":7},"attestation_state":"computed","paper":{"title":"On equality of central and class preserving automorphisms of finite p-groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Deepak Gumber, Hemant Kalra","submitted_at":"2011-06-02T06:55:15Z","abstract_excerpt":"Let $G$ be a finite non-abelian $p$-group, where $p$ is a prime. Let $\\mathrm{Aut}_c(G)$ and $\\mathrm{Aut}_z(G)$ respectively denote the group of all class preserving and central automorphisms of $G$. We give a necessary condition for $G$ such that $\\mathrm{Aut}_c(G)=\\mathrm{Aut}_z(G)$ and give necessary and sufficient conditions for $G$ with elementary abelian or cyclic center such that $\\mathrm{Aut}_c(G)=\\mathrm{Aut}_z(G).$ We also characterize all finite $p$-groups $G$ of order $\\leq p^7$ such that $\\mathrm{Aut}_c(G)=\\mathrm{Aut}_z(G)$ and complete the classification of all finite $p$-group"},"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":"1106.0373","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-06-02T06:55:15Z","cross_cats_sorted":[],"title_canon_sha256":"09e13ba54c94d4ab28c70b188c9a079c9701e78cad6d364fd756ef319cb3d9fe","abstract_canon_sha256":"c22e906f8fdf4dfdf3f35157e696c735e27b278087b5ceda326a910913d217d2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:45.631287Z","signature_b64":"YzrI4XE1xRydKbHk4r9wZNSKYfEqlKPs6X2G+bmO3g+oYM1/ITvUUBPxJ7Forxj/TODCRg3HJnsC1cdP9C0qBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"62867ff115ba38e6d117c13e3770c298b710346901d6c29f218f7870ab7d905c","last_reissued_at":"2026-05-18T03:20:45.630460Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:45.630460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On equality of central and class preserving automorphisms of finite p-groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Deepak Gumber, Hemant Kalra","submitted_at":"2011-06-02T06:55:15Z","abstract_excerpt":"Let $G$ be a finite non-abelian $p$-group, where $p$ is a prime. Let $\\mathrm{Aut}_c(G)$ and $\\mathrm{Aut}_z(G)$ respectively denote the group of all class preserving and central automorphisms of $G$. We give a necessary condition for $G$ such that $\\mathrm{Aut}_c(G)=\\mathrm{Aut}_z(G)$ and give necessary and sufficient conditions for $G$ with elementary abelian or cyclic center such that $\\mathrm{Aut}_c(G)=\\mathrm{Aut}_z(G).$ We also characterize all finite $p$-groups $G$ of order $\\leq p^7$ such that $\\mathrm{Aut}_c(G)=\\mathrm{Aut}_z(G)$ and complete the classification of all finite $p$-group"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.0373","kind":"arxiv","version":7},"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":"1106.0373","created_at":"2026-05-18T03:20:45.630601+00:00"},{"alias_kind":"arxiv_version","alias_value":"1106.0373v7","created_at":"2026-05-18T03:20:45.630601+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.0373","created_at":"2026-05-18T03:20:45.630601+00:00"},{"alias_kind":"pith_short_12","alias_value":"MKDH74IVXI4O","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_16","alias_value":"MKDH74IVXI4ONUIX","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_8","alias_value":"MKDH74IV","created_at":"2026-05-18T12:26:34.985390+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/MKDH74IVXI4ONUIXYE7DO4GCTC","json":"https://pith.science/pith/MKDH74IVXI4ONUIXYE7DO4GCTC.json","graph_json":"https://pith.science/api/pith-number/MKDH74IVXI4ONUIXYE7DO4GCTC/graph.json","events_json":"https://pith.science/api/pith-number/MKDH74IVXI4ONUIXYE7DO4GCTC/events.json","paper":"https://pith.science/paper/MKDH74IV"},"agent_actions":{"view_html":"https://pith.science/pith/MKDH74IVXI4ONUIXYE7DO4GCTC","download_json":"https://pith.science/pith/MKDH74IVXI4ONUIXYE7DO4GCTC.json","view_paper":"https://pith.science/paper/MKDH74IV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1106.0373&json=true","fetch_graph":"https://pith.science/api/pith-number/MKDH74IVXI4ONUIXYE7DO4GCTC/graph.json","fetch_events":"https://pith.science/api/pith-number/MKDH74IVXI4ONUIXYE7DO4GCTC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MKDH74IVXI4ONUIXYE7DO4GCTC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MKDH74IVXI4ONUIXYE7DO4GCTC/action/storage_attestation","attest_author":"https://pith.science/pith/MKDH74IVXI4ONUIXYE7DO4GCTC/action/author_attestation","sign_citation":"https://pith.science/pith/MKDH74IVXI4ONUIXYE7DO4GCTC/action/citation_signature","submit_replication":"https://pith.science/pith/MKDH74IVXI4ONUIXYE7DO4GCTC/action/replication_record"}},"created_at":"2026-05-18T03:20:45.630601+00:00","updated_at":"2026-05-18T03:20:45.630601+00:00"}