{"paper":{"title":"Pointlike sets for varieties determined by groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.FL"],"primary_cat":"math.GR","authors_text":"B. Steinberg, Samuel J. v. Gool","submitted_at":"2018-01-15T01:58:11Z","abstract_excerpt":"For a variety of finite groups $\\mathbf H$, let $\\overline{\\mathbf H}$ denote the variety of finite semigroups all of whose subgroups lie in $\\mathbf H$. We give a characterization of the subsets of a finite semigroup that are pointlike with respect to $\\overline{\\mathbf H}$. Our characterization is effective whenever $\\mathbf H$ has a decidable membership problem. In particular, the separation problem for $\\overline{\\mathbf H}$-languages is decidable for any decidable variety of finite groups $\\mathbf H$. This generalizes Henckell's theorem on decidability of aperiodic pointlikes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04638","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"}