{"paper":{"title":"Adjoining Roots and Rational Powers of Generators in PSL(2,\\RR) and Discreteness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Jane Gilman","submitted_at":"2017-05-09T21:00:03Z","abstract_excerpt":"Let $G$ be a finitely generated group of isometries of $\\HH^m$, hyperbolic $m$-space, for some positive integer $m$. %or equivalently elements of $PSL(2,\\CC)$.\n  The discreteness problem is to determine whether or not $G$ is discrete. Even in the case of a two generator non-elementary subgroup of $\\HH^2$ (equivalently $PSL(2,\\mathbb{R})$) the problem requires an algorithm \\cite{GM,JGtwo}. If $G$ is discrete, one can ask when adjoining an $n$th root of a generator results in a discrete group.\n  In this paper we address the issue for pairs of hyperbolic generators in $PSL(2, \\RR)$ with disjoint "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.03539","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"}