{"paper":{"title":"On the surjectivity of the power maps of a class of solvable groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Arunava Mandal, S.G. Dani","submitted_at":"2016-08-09T06:32:03Z","abstract_excerpt":"Let $G$ be a group containing a nilpotent normal subgroup $N$ with central series $\\{N_j\\}$, such that each $N_j/N_{j+1}$ is a $\\mathbb{F}$-vector space over a field $\\mathbb{F}$ and the action of $G$ on $N_j/N_{j+1}$ induced by the conjugation action is $\\mathbb{F}$-linear. For $k\\in \\mathbb N$ we describe a necessary and sufficient condition for all elements from any coset $xN$, $x\\in G$, to admit $k$-th roots in $G$, in terms of the action of $x$ on the quotients $N_j/N_{j+1}.$ This yields in particular a condition for surjectivity of the power maps, generalising various results known in sp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.02701","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"}