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In \\cite{BHW2}, it is proved that $\\mathcal{M}_{w}$ can be as a Chermak-Delgado lattice of a finite group if and only if $w=1+p^a$ for some positive integer $a$. Let $t$ be the number of abelian atoms in $\\mathcal{CD}(G)$. If $t>2$, then, according to \\cite{BHW2}, there exists a positive integer $b$ such that $t=p^b+1$. The converse is still an op"},"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":"1705.06456","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-05-18T08:15:01Z","cross_cats_sorted":[],"title_canon_sha256":"4ea4acaebec43aa193a1fc75dba0cf6b2382e1c13b52a40dc9f3ed0e25e01579","abstract_canon_sha256":"d95582c01ce43b0ddd749d5cbf025efa5313b785334435ec87aa4bf49c6d549c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:14.682028Z","signature_b64":"MtApjvWMN+YAJL3V3Q5QzBTdjojdCnnz4q9lp+2DkqBf0B7E2VrikOXrlE/6JdpnVQzw641dE0HXu71fUEexAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c5250df85356892c74f22fc8c47b0f5cd956cef84a0e50275af9e2ffc159824","last_reissued_at":"2026-05-18T00:44:14.681443Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:14.681443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Groups whose Chermak-Delgado lattice is a quasi-antichain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Lijian An","submitted_at":"2017-05-18T08:15:01Z","abstract_excerpt":"A quasiantichain is a lattice consisting of a maximum, a minimum, and the atoms of the lattice. 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