{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:XB467CXYCCVFD3BI6TR6XIUGSC","short_pith_number":"pith:XB467CXY","schema_version":"1.0","canonical_sha256":"b879ef8af810aa51ec28f4e3eba286908d3a03b788ff805df185feb1e5ea6a0a","source":{"kind":"arxiv","id":"1505.06293","version":6},"attestation_state":"computed","paper":{"title":"On $K_p$-series and varieties generated by wreath products of $p$-groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Vahagn H. Mikaelian","submitted_at":"2015-05-23T08:46:22Z","abstract_excerpt":"Let $A$ be a nilpotent $p$-group of finite exponent, and $B$ be an abelian $p$-groups of finite exponent. Then the wreath product $A {\\rm Wr} B$ generates the variety ${\\rm var}(A) {\\rm var}(B)$ if and only if the group $B$ contains a subgroup isomorphic to the direct product $C_{p^v}^\\infty$ of at least countably many copies of the cyclic group $C_{p^v}$ of order $p^v = \\exp{(B)}$. The obtained theorem continues our previous study of cases when ${\\rm var}(A {\\rm Wr} B ) = {\\rm var}(A){\\rm var}(B)$ holds for some other classes of groups $A$ and $B$ (abelian groups, finite groups, etc.)."},"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":"1505.06293","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-05-23T08:46:22Z","cross_cats_sorted":[],"title_canon_sha256":"aeaf87aaa2b518266a33fb5d34bd5e8868d9eeade9608ccbae996f97e8b39628","abstract_canon_sha256":"82e4f71e9913059e008eb6a83033df6a7ef0d8994ddb6b61aa0d5362d1976ac9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:02.958640Z","signature_b64":"uequs9vvI5TPkj9qaBrsMDNhPUHl+nskpqVd8Zug/tkLPeLaaWKhZ6pQmEVqz7K3OSRhryvyFa4Qy+CBkPntDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b879ef8af810aa51ec28f4e3eba286908d3a03b788ff805df185feb1e5ea6a0a","last_reissued_at":"2026-05-18T00:28:02.957918Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:02.957918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On $K_p$-series and varieties generated by wreath products of $p$-groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Vahagn H. Mikaelian","submitted_at":"2015-05-23T08:46:22Z","abstract_excerpt":"Let $A$ be a nilpotent $p$-group of finite exponent, and $B$ be an abelian $p$-groups of finite exponent. Then the wreath product $A {\\rm Wr} B$ generates the variety ${\\rm var}(A) {\\rm var}(B)$ if and only if the group $B$ contains a subgroup isomorphic to the direct product $C_{p^v}^\\infty$ of at least countably many copies of the cyclic group $C_{p^v}$ of order $p^v = \\exp{(B)}$. The obtained theorem continues our previous study of cases when ${\\rm var}(A {\\rm Wr} B ) = {\\rm var}(A){\\rm var}(B)$ holds for some other classes of groups $A$ and $B$ (abelian groups, finite groups, etc.)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06293","kind":"arxiv","version":6},"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":"1505.06293","created_at":"2026-05-18T00:28:02.958031+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.06293v6","created_at":"2026-05-18T00:28:02.958031+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.06293","created_at":"2026-05-18T00:28:02.958031+00:00"},{"alias_kind":"pith_short_12","alias_value":"XB467CXYCCVF","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_16","alias_value":"XB467CXYCCVFD3BI","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_8","alias_value":"XB467CXY","created_at":"2026-05-18T12:29:50.041715+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/XB467CXYCCVFD3BI6TR6XIUGSC","json":"https://pith.science/pith/XB467CXYCCVFD3BI6TR6XIUGSC.json","graph_json":"https://pith.science/api/pith-number/XB467CXYCCVFD3BI6TR6XIUGSC/graph.json","events_json":"https://pith.science/api/pith-number/XB467CXYCCVFD3BI6TR6XIUGSC/events.json","paper":"https://pith.science/paper/XB467CXY"},"agent_actions":{"view_html":"https://pith.science/pith/XB467CXYCCVFD3BI6TR6XIUGSC","download_json":"https://pith.science/pith/XB467CXYCCVFD3BI6TR6XIUGSC.json","view_paper":"https://pith.science/paper/XB467CXY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.06293&json=true","fetch_graph":"https://pith.science/api/pith-number/XB467CXYCCVFD3BI6TR6XIUGSC/graph.json","fetch_events":"https://pith.science/api/pith-number/XB467CXYCCVFD3BI6TR6XIUGSC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XB467CXYCCVFD3BI6TR6XIUGSC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XB467CXYCCVFD3BI6TR6XIUGSC/action/storage_attestation","attest_author":"https://pith.science/pith/XB467CXYCCVFD3BI6TR6XIUGSC/action/author_attestation","sign_citation":"https://pith.science/pith/XB467CXYCCVFD3BI6TR6XIUGSC/action/citation_signature","submit_replication":"https://pith.science/pith/XB467CXYCCVFD3BI6TR6XIUGSC/action/replication_record"}},"created_at":"2026-05-18T00:28:02.958031+00:00","updated_at":"2026-05-18T00:28:02.958031+00:00"}