{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:CCMGV2NGZXM45M4CK5O532OSQL","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":"fe7d067ad61ff67883031f32e384e907d8c68ab11867c806d52da8c4222ffea3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-06-27T11:36:33Z","title_canon_sha256":"f06a66ccc8edc7092e56fcc55c8eae1bce1844152e64fb03392b5363d416158f"},"schema_version":"1.0","source":{"id":"1306.6470","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.6470","created_at":"2026-05-18T03:13:33Z"},{"alias_kind":"arxiv_version","alias_value":"1306.6470v3","created_at":"2026-05-18T03:13:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.6470","created_at":"2026-05-18T03:13:33Z"},{"alias_kind":"pith_short_12","alias_value":"CCMGV2NGZXM4","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CCMGV2NGZXM45M4C","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CCMGV2NG","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:2ba1728f739472de291f6292b93a0d4bc79b3b68bdfbc439f41688f599e8c9f7","target":"graph","created_at":"2026-05-18T03:13:33Z","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":"There are several examples in the literature of finite non-abelian $p$-groups whose automorphism group is abelian. For some time only examples that were special $p$-groups were known, until Jain and Yadav [JY12] and Jain, Rai and Yadav [JRY13] constructed several non-special examples. In this paper we show how a simple module-theoretic approach allows the construction of non-special examples, starting from special ones constructed by several authors, while at the same time avoiding further direct calculations.","authors_text":"A. Caranti","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-06-27T11:36:33Z","title":"A module-theoretic approach to abelian automorphism groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.6470","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:f4557e7c3a8f6450cb3a32442bfaafdb209bbe29e9f85384ad10b32d21e79afc","target":"record","created_at":"2026-05-18T03:13:33Z","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":"fe7d067ad61ff67883031f32e384e907d8c68ab11867c806d52da8c4222ffea3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-06-27T11:36:33Z","title_canon_sha256":"f06a66ccc8edc7092e56fcc55c8eae1bce1844152e64fb03392b5363d416158f"},"schema_version":"1.0","source":{"id":"1306.6470","kind":"arxiv","version":3}},"canonical_sha256":"10986ae9a6cdd9ceb382575ddde9d282c59edd33116b61562d927ab3996d3035","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"10986ae9a6cdd9ceb382575ddde9d282c59edd33116b61562d927ab3996d3035","first_computed_at":"2026-05-18T03:13:33.500100Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:13:33.500100Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wygRuPijU9GZf/osm2dlvD39iuN+PV4cH6JSRxNvgf/C0MsjL1lmr2G8cxDzOWvv6RePfQYfU1PLUItYuFl8Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:13:33.500904Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.6470","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f4557e7c3a8f6450cb3a32442bfaafdb209bbe29e9f85384ad10b32d21e79afc","sha256:2ba1728f739472de291f6292b93a0d4bc79b3b68bdfbc439f41688f599e8c9f7"],"state_sha256":"99959ae39be4291dc8e7d5b6137957e9ec799708724cd5ca5a359ec108e0c7af"}