{"paper":{"title":"A generalization of Neumann's Question","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"A. Ahmadkhah, M. Zarrin, S. Marzang","submitted_at":"2017-12-30T10:52:59Z","abstract_excerpt":"Let $G$ be a group, $m\\geq2$ and $n\\geq1$. We say that $G$ is an $\\mathcal{T}(m,n)$-group if for every $m$ subsets $X_1, X_2, \\dots, X_m$ of $G$ of cardinality $n$, there exists $i\\neq j$ and $x_i \\in X_i, x_j \\in X_j$ such that $x_ix_j=x_jx_i$. In this paper, we give some examples of finite and infinite non-abelian $\\mathcal{T}(m,n)$-groups and we discuss finiteness and commutativity of such groups. We also show solvability length of a solvable $\\mathcal{T}(m,n)$-group is bounded in terms of $m$ and $n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00113","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"}