{"paper":{"title":"Translation equivalent elements in free groups","license":"","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Donghi Lee","submitted_at":"2006-04-20T03:10:03Z","abstract_excerpt":"Let F_n be a free group of rank n>1. Two elements g, h in F_n are said to be translation equivalent in F_n if the cyclic length of \\phi(g) equals the cyclic length of \\phi(h) for every automorphism \\phi of F_n. Let F(a, b) be the free group generated by {a, b} and let w(a,b) be an arbitrary word in F(a,b). We prove that w(g, h) and w(h, g) are translation equivalent in F_n whenever g, h \\in F_n are translation equivalent in F_n, which hereby gives an affirmative solution to problem F38b in the online version (http://www.grouptheory.info) of [1]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0604435","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"}