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Hall), then $\\Aut_c(G) \\cong \\Aut_c(H)$. Finally we study class preserving automorphisms of groups of order $p^5$ and prove that $\\Aut_c(G) = \\Inn(G)$ for all the groups of order $p^5$ except two isoclinism families."},"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":"math/0608535","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2006-08-22T07:27:08Z","cross_cats_sorted":[],"title_canon_sha256":"0ab64881e4ed642aa2ee6af6934fd401b13f012064b5455169bf8915b721cf0e","abstract_canon_sha256":"2b59bbb1415b050822ae1d8f9e5eea796131b64c9af7fdeb580c3585a1ff9b38"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:12:32.584388Z","signature_b64":"Q/LdHMdHxWKBmN348Yx4fgtBUuV9dr5Niy3piASRTTQMlHvVgmhA3xqt1slnuyI4eleBzRniJLqtc2CT0XqEAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ad4e05234e62c1ad0f5bfb20cab1e944d97fb65d0a59c849eeec2ee2b6bbc36","last_reissued_at":"2026-05-18T04:12:32.583933Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:12:32.583933Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Automorphisms of Some Finite $p$-groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Manoj K. Yadav","submitted_at":"2006-08-22T07:27:08Z","abstract_excerpt":"We give a sufficient condition on a finite $p$-group $G$ of nilpotency class 2 so that $\\Aut_c(G) = \\Inn(G)$, where $\\Aut_c(G)$ and $\\Inn(G)$ denote the group of all class preserving automorphisms and inner automorphisms of $G$ respectively. Next we prove that if $G$ and $H$ are two isoclinic finite groups (in the sense of P. Hall), then $\\Aut_c(G) \\cong \\Aut_c(H)$. Finally we study class preserving automorphisms of groups of order $p^5$ and prove that $\\Aut_c(G) = \\Inn(G)$ for all the groups of order $p^5$ except two isoclinism families."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0608535","kind":"arxiv","version":3},"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":"math/0608535","created_at":"2026-05-18T04:12:32.583995+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0608535v3","created_at":"2026-05-18T04:12:32.583995+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0608535","created_at":"2026-05-18T04:12:32.583995+00:00"},{"alias_kind":"pith_short_12","alias_value":"DLKOAURU4YWB","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_16","alias_value":"DLKOAURU4YWBVUHV","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_8","alias_value":"DLKOAURU","created_at":"2026-05-18T12:25:53.939244+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/DLKOAURU4YWBVUHVX6ZAZKY6SR","json":"https://pith.science/pith/DLKOAURU4YWBVUHVX6ZAZKY6SR.json","graph_json":"https://pith.science/api/pith-number/DLKOAURU4YWBVUHVX6ZAZKY6SR/graph.json","events_json":"https://pith.science/api/pith-number/DLKOAURU4YWBVUHVX6ZAZKY6SR/events.json","paper":"https://pith.science/paper/DLKOAURU"},"agent_actions":{"view_html":"https://pith.science/pith/DLKOAURU4YWBVUHVX6ZAZKY6SR","download_json":"https://pith.science/pith/DLKOAURU4YWBVUHVX6ZAZKY6SR.json","view_paper":"https://pith.science/paper/DLKOAURU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0608535&json=true","fetch_graph":"https://pith.science/api/pith-number/DLKOAURU4YWBVUHVX6ZAZKY6SR/graph.json","fetch_events":"https://pith.science/api/pith-number/DLKOAURU4YWBVUHVX6ZAZKY6SR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DLKOAURU4YWBVUHVX6ZAZKY6SR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DLKOAURU4YWBVUHVX6ZAZKY6SR/action/storage_attestation","attest_author":"https://pith.science/pith/DLKOAURU4YWBVUHVX6ZAZKY6SR/action/author_attestation","sign_citation":"https://pith.science/pith/DLKOAURU4YWBVUHVX6ZAZKY6SR/action/citation_signature","submit_replication":"https://pith.science/pith/DLKOAURU4YWBVUHVX6ZAZKY6SR/action/replication_record"}},"created_at":"2026-05-18T04:12:32.583995+00:00","updated_at":"2026-05-18T04:12:32.583995+00:00"}