{"paper":{"title":"On the density of images of the power maps in Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Arunava Mandal, Saurav Bhaumik","submitted_at":"2017-01-02T08:08:29Z","abstract_excerpt":"Let $G$ be a connected Lie group. In this paper, we study the density of the images of individual power maps $P_k:G\\to G:g\\mapsto g^k$. We give criteria for the density of $P_k(G)$ in terms of regular elements, as well as Cartan subgroups. In fact, we prove that if ${\\rm Reg}(G)$ is the set of regular elements of $G$, then $P_k(G)\\cap {\\rm Reg}(G)$ is closed in ${\\rm Reg}(G)$. On the other hand, the weak exponentiality of $G$ turns out to be equivalent to the density of all the power maps $P_k$. In linear Lie groups, weak exponentiality reduces to the density of $P_2(G)$. We also prove that th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00331","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"}