{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:XZCHSKRM2YS3KJK6VVSMGJU3WU","short_pith_number":"pith:XZCHSKRM","canonical_record":{"source":{"id":"1501.03090","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-01-13T17:57:37Z","cross_cats_sorted":[],"title_canon_sha256":"7bae43003fccfc51b9ebd27c3538ca03ccb5b2debb56927900c4611dc92faea6","abstract_canon_sha256":"e787f2902e5dbab0af75cc613b13b888b4b26069e40f4b8eff32b9ac7252ea59"},"schema_version":"1.0"},"canonical_sha256":"be44792a2cd625b5255ead64c3269bb50bc32a2853b49efaa62d0714e02a892b","source":{"kind":"arxiv","id":"1501.03090","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.03090","created_at":"2026-05-18T02:28:04Z"},{"alias_kind":"arxiv_version","alias_value":"1501.03090v3","created_at":"2026-05-18T02:28:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.03090","created_at":"2026-05-18T02:28:04Z"},{"alias_kind":"pith_short_12","alias_value":"XZCHSKRM2YS3","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XZCHSKRM2YS3KJK6","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XZCHSKRM","created_at":"2026-05-18T12:29:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:XZCHSKRM2YS3KJK6VVSMGJU3WU","target":"record","payload":{"canonical_record":{"source":{"id":"1501.03090","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-01-13T17:57:37Z","cross_cats_sorted":[],"title_canon_sha256":"7bae43003fccfc51b9ebd27c3538ca03ccb5b2debb56927900c4611dc92faea6","abstract_canon_sha256":"e787f2902e5dbab0af75cc613b13b888b4b26069e40f4b8eff32b9ac7252ea59"},"schema_version":"1.0"},"canonical_sha256":"be44792a2cd625b5255ead64c3269bb50bc32a2853b49efaa62d0714e02a892b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:04.773958Z","signature_b64":"nxfqH01pRFmGZAhE/YcbXpj6Pmtrqtp2M6w3UBivh1JpDx440b6Uvc2QQtpSyOrhMmlTMTeRrGNvDQJlTCzOCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"be44792a2cd625b5255ead64c3269bb50bc32a2853b49efaa62d0714e02a892b","last_reissued_at":"2026-05-18T02:28:04.773374Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:04.773374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.03090","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:28:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NuAZt2fT3Ib4EWlEwPuAKnSpIsdpRs1mxDvvCSCGkofCiORBUp/9m1RsJGBQsOZx9dFVOTPHFQ5Gqis5801jCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T04:57:45.952095Z"},"content_sha256":"c3e6597c21465b4f1d51d297e43128959790fbd4faf352b4e1daecde183cda71","schema_version":"1.0","event_id":"sha256:c3e6597c21465b4f1d51d297e43128959790fbd4faf352b4e1daecde183cda71"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:XZCHSKRM2YS3KJK6VVSMGJU3WU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A generalization of 2-Baer groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"A. Tortora, L.-C. Kappe","submitted_at":"2015-01-13T17:57:37Z","abstract_excerpt":"A group in which all cyclic subgroups are 2-subnormal is called a 2-Baer group. The topic of this paper are generalized 2-Baer groups, i.e. groups in which the non-2-subnormal cyclic subgroups generate a proper subgroup of the group. If this subgroup is non-trivial, the group is called a generalized T_2-group. In particular, we provide structure results for such groups, investigate their nilpotency class and construct examples of finite p-groups which are generalized T_2-groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.03090","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:28:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CkeQwSiiJW2y3gxsWicb3szZLiEb/EYUvAs5bg7dBjy1EBzIT3ymNGW9spJTYc4GTcUwwsB3UhaauzO3xNvMDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T04:57:45.952721Z"},"content_sha256":"d66bed385f5aa1eb3d640d0b4fa8090ce449744a0a3991c6a103b32d67cdfd5f","schema_version":"1.0","event_id":"sha256:d66bed385f5aa1eb3d640d0b4fa8090ce449744a0a3991c6a103b32d67cdfd5f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XZCHSKRM2YS3KJK6VVSMGJU3WU/bundle.json","state_url":"https://pith.science/pith/XZCHSKRM2YS3KJK6VVSMGJU3WU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XZCHSKRM2YS3KJK6VVSMGJU3WU/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T04:57:45Z","links":{"resolver":"https://pith.science/pith/XZCHSKRM2YS3KJK6VVSMGJU3WU","bundle":"https://pith.science/pith/XZCHSKRM2YS3KJK6VVSMGJU3WU/bundle.json","state":"https://pith.science/pith/XZCHSKRM2YS3KJK6VVSMGJU3WU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XZCHSKRM2YS3KJK6VVSMGJU3WU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:XZCHSKRM2YS3KJK6VVSMGJU3WU","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":"e787f2902e5dbab0af75cc613b13b888b4b26069e40f4b8eff32b9ac7252ea59","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-01-13T17:57:37Z","title_canon_sha256":"7bae43003fccfc51b9ebd27c3538ca03ccb5b2debb56927900c4611dc92faea6"},"schema_version":"1.0","source":{"id":"1501.03090","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.03090","created_at":"2026-05-18T02:28:04Z"},{"alias_kind":"arxiv_version","alias_value":"1501.03090v3","created_at":"2026-05-18T02:28:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.03090","created_at":"2026-05-18T02:28:04Z"},{"alias_kind":"pith_short_12","alias_value":"XZCHSKRM2YS3","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XZCHSKRM2YS3KJK6","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XZCHSKRM","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:d66bed385f5aa1eb3d640d0b4fa8090ce449744a0a3991c6a103b32d67cdfd5f","target":"graph","created_at":"2026-05-18T02:28:04Z","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":"A group in which all cyclic subgroups are 2-subnormal is called a 2-Baer group. The topic of this paper are generalized 2-Baer groups, i.e. groups in which the non-2-subnormal cyclic subgroups generate a proper subgroup of the group. If this subgroup is non-trivial, the group is called a generalized T_2-group. In particular, we provide structure results for such groups, investigate their nilpotency class and construct examples of finite p-groups which are generalized T_2-groups.","authors_text":"A. Tortora, L.-C. Kappe","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-01-13T17:57:37Z","title":"A generalization of 2-Baer groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.03090","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:c3e6597c21465b4f1d51d297e43128959790fbd4faf352b4e1daecde183cda71","target":"record","created_at":"2026-05-18T02:28:04Z","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":"e787f2902e5dbab0af75cc613b13b888b4b26069e40f4b8eff32b9ac7252ea59","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-01-13T17:57:37Z","title_canon_sha256":"7bae43003fccfc51b9ebd27c3538ca03ccb5b2debb56927900c4611dc92faea6"},"schema_version":"1.0","source":{"id":"1501.03090","kind":"arxiv","version":3}},"canonical_sha256":"be44792a2cd625b5255ead64c3269bb50bc32a2853b49efaa62d0714e02a892b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be44792a2cd625b5255ead64c3269bb50bc32a2853b49efaa62d0714e02a892b","first_computed_at":"2026-05-18T02:28:04.773374Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:04.773374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nxfqH01pRFmGZAhE/YcbXpj6Pmtrqtp2M6w3UBivh1JpDx440b6Uvc2QQtpSyOrhMmlTMTeRrGNvDQJlTCzOCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:04.773958Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.03090","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c3e6597c21465b4f1d51d297e43128959790fbd4faf352b4e1daecde183cda71","sha256:d66bed385f5aa1eb3d640d0b4fa8090ce449744a0a3991c6a103b32d67cdfd5f"],"state_sha256":"ab1fdedb910b15e9bac9bd4f4d2c2a373bbdd216945db9194835727dd4a49690"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eHpBFtl1IAU+RvxzxQdFXttV3iTWod1tEwA7J1HJq3IilB8b8yzF0mp28M+K0Bx0uY7b1kzu4+1dlUfu0ciXAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T04:57:45.956468Z","bundle_sha256":"28c5fda7645a2f16b79ee5125631c503acdf1208329fdd12477d8e3d951fc125"}}