{"paper":{"title":"On semilinear sets and asymptotically approximate groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.GR"],"primary_cat":"math.NT","authors_text":"Arindam Biswas, Wolfgang Alexander Moens","submitted_at":"2019-02-15T10:36:33Z","abstract_excerpt":"Let $G$ be any group and $A$ be an arbitrary subset of $G$ (not necessarily symmetric and not necessarily containing the identity). The $h$-fold product set of $A$ is defined as $$A^{h} :=\\lbrace a_{1}.a_{2}...a_{h} : a_{1},\\ldots,a_n \\in A \\rbrace.$$ Nathanson considered the concept of an asymptotic approximate group. Let $r,l \\in \\mathbb{N}$. The set $A$ is said to be an $(r,l)$ approximate group in $G$ if there exists a subset $X$ in $G$ such that $|X|\\leqslant l$ and $A^{r}\\subseteq XA$. The set $A$ is an asymptotic $(r,l)$-approximate group if the product set $A^{h}$ is an $(r,l)$-approxi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.05757","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"}