{"paper":{"title":"Criteria for nilpotency of groups via partitons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"L.J. Taghvasani, M. Zarrin","submitted_at":"2018-04-18T12:33:33Z","abstract_excerpt":"Let $G$ be a finite group and $S< G$. A cover for a group $G$ is a collection of subgroups of $G$ whose union is $G$.  We use the term $n$-cover for a cover with $n$ members. A cover $\\Pi =\\{H_1, H_2, \\dots, H_n\\}$ is said to be a  strict $\\mathit{S}$-partition of $G$ if $H_i\\cap H_j= S$ for $i\\neq j$ and $\\Pi$ is said an equal strict $\\mathit{S}$-partition (or $ES$-partition ) of $G$, if $\\Pi$ is a strict $S$-partition and $|H_i|=|H_j|$ for all $i\\neq j$. If $S$ is the identity subgroup and $G$ has a strict $S$-partition (equal strict $\\mathit{S}$-partition), then we say that $G$ has a partit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.06684","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"}