{"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. The width of a quasiantichian is the number of atoms. For a positive integer $w$ ($\\ge 3$), a quasiantichain of width $w$ is denoted by $\\mathcal{M}_{w}$. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.06456","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"}