{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:DRCKPTPK3QYF4KNJ6UNIKL7EOO","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":"ce4159ed5b7ef9f0d98ec266b128b09b1d1e735503a2b4bf1c7d137b4672b342","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-11-15T21:58:26Z","title_canon_sha256":"e80654209bc24674b1b8264c52b03418bdbe1ef04b066a010f093e0b427180dc"},"schema_version":"1.0","source":{"id":"1411.4190","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.4190","created_at":"2026-05-18T02:32:30Z"},{"alias_kind":"arxiv_version","alias_value":"1411.4190v2","created_at":"2026-05-18T02:32:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.4190","created_at":"2026-05-18T02:32:30Z"},{"alias_kind":"pith_short_12","alias_value":"DRCKPTPK3QYF","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DRCKPTPK3QYF4KNJ","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DRCKPTPK","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:61bbf06f4042cd1a86c631e92aa420bd71d37225cc66201ade698e49cbc58ae3","target":"graph","created_at":"2026-05-18T02:32:30Z","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":"We investigate the endomorphism monoids of certain finite $p$-groups of order $p^8$ first studied by Jonah and Konvisser in 1975 as examples for finite $p$-groups with abelian automorphism group, and we show some necessary conditions for a finite $p$-group to have commutative endomorphism monoid. As a by-product, apart from formulas for the number of conjugacy classes of endomorphisms of said groups, we will be able to derive the following: There exist nonabelian groups with commutative endomorphism monoid, and having commutative endomorphism monoid is a group property strictly stronger than h","authors_text":"Alexander Bors","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-11-15T21:58:26Z","title":"On the endomorphism monoids of some groups with abelian automorphism group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4190","kind":"arxiv","version":2},"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":"sha256:043c54edb0da76ab79c7fa1bcf81d6b6bf2d058053d00674c69450013a1498c8","target":"record","created_at":"2026-05-18T02:32:30Z","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":"ce4159ed5b7ef9f0d98ec266b128b09b1d1e735503a2b4bf1c7d137b4672b342","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-11-15T21:58:26Z","title_canon_sha256":"e80654209bc24674b1b8264c52b03418bdbe1ef04b066a010f093e0b427180dc"},"schema_version":"1.0","source":{"id":"1411.4190","kind":"arxiv","version":2}},"canonical_sha256":"1c44a7cdeadc305e29a9f51a852fe4738b9a1e7900b3c5c5ed55de31f2f17643","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c44a7cdeadc305e29a9f51a852fe4738b9a1e7900b3c5c5ed55de31f2f17643","first_computed_at":"2026-05-18T02:32:30.426649Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:30.426649Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5N1PLUTfsbjSvWtOLUjOHGEixVqcAOgfE3p1HPIVlmbN5nmmWE7r+FjcLT93KKEQgPoealErE6PlRYHsshG8Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:30.426992Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.4190","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:043c54edb0da76ab79c7fa1bcf81d6b6bf2d058053d00674c69450013a1498c8","sha256:61bbf06f4042cd1a86c631e92aa420bd71d37225cc66201ade698e49cbc58ae3"],"state_sha256":"a6e782b90767eb389d836c4189e1020aeb8dc0b136059413ea89900b7cfed6e1"}