{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:PDRV7UXCN4VNEWUKC2QXBRSW3C","short_pith_number":"pith:PDRV7UXC","schema_version":"1.0","canonical_sha256":"78e35fd2e26f2ad25a8a16a170c656d8a64cf9756f89f7ebf0125c134800a063","source":{"kind":"arxiv","id":"1801.01977","version":1},"attestation_state":"computed","paper":{"title":"On varieties of groups generated by wreath products of abelian groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Vahagn H. Mikaelian","submitted_at":"2018-01-06T06:51:30Z","abstract_excerpt":"Generalizing results of Higman and Houghton on varieties generated by wreath products of finite cycles, we prove that the (direct or cartesian) wreath product of arbitrary abelian groups $A$ and $B$ generates the product variety $var (A) \\cdot var (B)$ if and only if one of the groups $A$ and $B$ is not of finite exponent, or if $A$ and $B$ are of finite exponents $m$ and $n$ respectively and for all primes $p$ dividing both $m$ and $n$, the factors $B[p^k]/B[p^{k-1}]$ are infinite, where $B[s]=\\langle b\\in B|\\,b^{s}=1 \\rangle$ and where $p^k$ is the highest power of $p$ dividing $n$."},"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":"1801.01977","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-01-06T06:51:30Z","cross_cats_sorted":[],"title_canon_sha256":"d4eef4d82205a5fcc234602f1a8cf55362819f565ceb7de3cf9880724fad27f9","abstract_canon_sha256":"30f58f72ff32e188d892c05924ca1f953d411122cfaa1340748363a786206f70"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:35.321222Z","signature_b64":"OZ/43Swsz14XiaTVNcU1ZLVh9D+lpfNYBM2FrRrnF1GgS48NjI2OGg4smdlQ2oW+nH6/SRaP2dqImg3gMebCCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78e35fd2e26f2ad25a8a16a170c656d8a64cf9756f89f7ebf0125c134800a063","last_reissued_at":"2026-05-18T00:26:35.320575Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:35.320575Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On varieties of groups generated by wreath products of abelian groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Vahagn H. Mikaelian","submitted_at":"2018-01-06T06:51:30Z","abstract_excerpt":"Generalizing results of Higman and Houghton on varieties generated by wreath products of finite cycles, we prove that the (direct or cartesian) wreath product of arbitrary abelian groups $A$ and $B$ generates the product variety $var (A) \\cdot var (B)$ if and only if one of the groups $A$ and $B$ is not of finite exponent, or if $A$ and $B$ are of finite exponents $m$ and $n$ respectively and for all primes $p$ dividing both $m$ and $n$, the factors $B[p^k]/B[p^{k-1}]$ are infinite, where $B[s]=\\langle b\\in B|\\,b^{s}=1 \\rangle$ and where $p^k$ is the highest power of $p$ dividing $n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.01977","kind":"arxiv","version":1},"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":"1801.01977","created_at":"2026-05-18T00:26:35.320655+00:00"},{"alias_kind":"arxiv_version","alias_value":"1801.01977v1","created_at":"2026-05-18T00:26:35.320655+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.01977","created_at":"2026-05-18T00:26:35.320655+00:00"},{"alias_kind":"pith_short_12","alias_value":"PDRV7UXCN4VN","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_16","alias_value":"PDRV7UXCN4VNEWUK","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_8","alias_value":"PDRV7UXC","created_at":"2026-05-18T12:32:43.782077+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/PDRV7UXCN4VNEWUKC2QXBRSW3C","json":"https://pith.science/pith/PDRV7UXCN4VNEWUKC2QXBRSW3C.json","graph_json":"https://pith.science/api/pith-number/PDRV7UXCN4VNEWUKC2QXBRSW3C/graph.json","events_json":"https://pith.science/api/pith-number/PDRV7UXCN4VNEWUKC2QXBRSW3C/events.json","paper":"https://pith.science/paper/PDRV7UXC"},"agent_actions":{"view_html":"https://pith.science/pith/PDRV7UXCN4VNEWUKC2QXBRSW3C","download_json":"https://pith.science/pith/PDRV7UXCN4VNEWUKC2QXBRSW3C.json","view_paper":"https://pith.science/paper/PDRV7UXC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1801.01977&json=true","fetch_graph":"https://pith.science/api/pith-number/PDRV7UXCN4VNEWUKC2QXBRSW3C/graph.json","fetch_events":"https://pith.science/api/pith-number/PDRV7UXCN4VNEWUKC2QXBRSW3C/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PDRV7UXCN4VNEWUKC2QXBRSW3C/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PDRV7UXCN4VNEWUKC2QXBRSW3C/action/storage_attestation","attest_author":"https://pith.science/pith/PDRV7UXCN4VNEWUKC2QXBRSW3C/action/author_attestation","sign_citation":"https://pith.science/pith/PDRV7UXCN4VNEWUKC2QXBRSW3C/action/citation_signature","submit_replication":"https://pith.science/pith/PDRV7UXCN4VNEWUKC2QXBRSW3C/action/replication_record"}},"created_at":"2026-05-18T00:26:35.320655+00:00","updated_at":"2026-05-18T00:26:35.320655+00:00"}