{"paper":{"title":"Quasi-Antichain Chermak-Delgado Lattices of Finite Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Ben Brewster, Elizabeth Wilcox, Peter Hauck","submitted_at":"2014-07-23T13:50:29Z","abstract_excerpt":"The Chermak-Delgado lattice of a finite group is a dual, modular sublattice of the subgroup lattice of the group. This paper considers groups with a quasi-antichain interval in the Chermak-Delgado lattice, ultimately proving that if there is a quasi-antichain interval between $L$ and $H$ with $L \\leq H$ then there exists a prime $p$ such that the quotient $H / L$ is an elementary abelian $p$-group and the number of atoms in the quasi-antichain is one more than a power of $p$. In the case where the Chermak-Delgado lattice of the entire group is a quasi-antichain, the relationship between the nu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.6215","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"}