{"paper":{"title":"Detecting ends of residually finite groups in profinite completions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Owen Cotton-Barratt","submitted_at":"2012-05-01T22:31:08Z","abstract_excerpt":"Let $\\C$ be a variety of finite groups. We use profinite Bass--Serre theory to show that if $u:H\\hookrightarrow G$ is a map of finitely generated residually $\\C$ groups such that the induced map $\\hat{u}:\\hat{H}\\rightarrow\\hat{G}$ is a surjection of the pro-$\\C$ completions, and $G$ has more than one end, then $H$ has the same number of ends as $G$. However if $G$ has one end the number of ends of $H$ may be larger; we observe cases where this occurs for $\\C$ the class of finite $p$-groups.\n  We produce a monomorphism of groups $u:H\\hookrightarrow G$ such that: either $G$ is hyperbolic but not"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.0271","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"}