{"paper":{"title":"On F-inverse covers of finite-above inverse monoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"M\\'aria B. Szendrei, N\\'ora Szak\\'acs","submitted_at":"2015-11-30T16:36:13Z","abstract_excerpt":"Finite-above inverse monoids are a common generalization of finite inverse monoids and Margolis--Meakin expansions of groups. Given a finite-above $E$-unitary inverse monoid $M$ and a group variety $\\mathit{U}$, we find a condition for $M$ and $\\mathit{U}$, involving a construction of descending chains of graphs, which is equivalent to $M$ having an $F$-inverse cover via $\\mathit{U}$. In the special case where $\\mathit{U}=\\mathit{Ab}$, the variety of Abelian groups, we apply this condition to get a simple sufficient condition for $M$ to have no $F$-inverse cover via $\\mathit{Ab}$, formulated b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.09378","kind":"arxiv","version":2},"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"}