{"paper":{"title":"The Waring problem for Lie groups and Chevalley groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Aner Shalev, Chun Yin Hui, Michael Larsen","submitted_at":"2014-04-18T13:37:42Z","abstract_excerpt":"The classical Waring problem deals with expressing every natural number as a sum of g(k) k-th powers. Similar problems were recently studied in group theory, where we aim to present group elements as short products of values of a given non-trivial word w. In this paper we study this problem for Lie groups and Chevalley groups over infinite fields. We show that for a fixed non-trivial word w and for a classical connected real compact Lie group G of sufficiently large rank we have w(G)^2=G, namely every element of G is a product of 2 values of w. We prove a similar result for non-compact Lie gro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4786","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"}