{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:YAMW56PZW4N6JVSWXA4I4P5XCB","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a948c1310d3a7156eae1ccea567da44ed9fc79a74e920679e6a60b7da3649878","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-02-14T18:20:41Z","title_canon_sha256":"8192cfa1beb8f60ab849acbe3be847de50bf410b77fc00d3b7573c68c168f4b7"},"schema_version":"1.0","source":{"id":"1302.3499","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.3499","created_at":"2026-05-18T02:42:29Z"},{"alias_kind":"arxiv_version","alias_value":"1302.3499v3","created_at":"2026-05-18T02:42:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.3499","created_at":"2026-05-18T02:42:29Z"},{"alias_kind":"pith_short_12","alias_value":"YAMW56PZW4N6","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"YAMW56PZW4N6JVSW","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"YAMW56PZ","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:7877d9b74ed40304a8ae3adf576ecb6a748f20f61517a75b23ebb6f4c5ccf673","target":"graph","created_at":"2026-05-18T02:42:29Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Suppose that a finite $p$-group $P$ admits a Frobenius group of automorphisms $FH$ with kernel $F$ that is a cyclic $p$-group and with complement $H$. It is proved that if the fixed-point subgroup $C_P(H)$ of the complement is nilpotent of class $c$, then $P$ has a characteristic subgroup of index bounded in terms of $c$, $|C_P(F)|$, and $|F|$ whose nilpotency class is bounded in terms of $c$ and $|H|$ only. Examples show that the condition of $F$ being cyclic is essential. The proof is based on a Lie ring method and a theorem of the authors and P. Shumyatsky about Lie rings with a metacyclic ","authors_text":"E. I. Khukhro, N. Yu. Makarenko","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-02-14T18:20:41Z","title":"Finite p-groups with a Frobenius group of automorphisms whose kernel is a cyclic p-group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.3499","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:000781653b1885b5cfd8fd7fe635b99a1d477bd5d1336a29d02e1063e18cb9a9","target":"record","created_at":"2026-05-18T02:42:29Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a948c1310d3a7156eae1ccea567da44ed9fc79a74e920679e6a60b7da3649878","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-02-14T18:20:41Z","title_canon_sha256":"8192cfa1beb8f60ab849acbe3be847de50bf410b77fc00d3b7573c68c168f4b7"},"schema_version":"1.0","source":{"id":"1302.3499","kind":"arxiv","version":3}},"canonical_sha256":"c0196ef9f9b71be4d656b8388e3fb71051080900f3b331e3451b683e87dd3a32","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c0196ef9f9b71be4d656b8388e3fb71051080900f3b331e3451b683e87dd3a32","first_computed_at":"2026-05-18T02:42:29.120185Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:29.120185Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KAOFgEIAOujc1Jl2F6CLrELzPMeCiEFPCKrW/0tFcZ2lcP9iiT1+TV0eGkv5d14J4t2p5ujGBWwxew9ycfpDDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:29.121084Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.3499","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:000781653b1885b5cfd8fd7fe635b99a1d477bd5d1336a29d02e1063e18cb9a9","sha256:7877d9b74ed40304a8ae3adf576ecb6a748f20f61517a75b23ebb6f4c5ccf673"],"state_sha256":"e132b6d960fc969e67b3e2fb6023dae48d4bf27daf94c1f4eca073057d126c84"}