Bardakov, V. G. Computing the commutator length in free groups. (English. Russian original) Zbl 0960.20019 Algebra Logika 39, No. 4, 395-440 (2000); translation in Algebra Logic 39, No. 4, 224-251 (2000). Let \(F\) be a free group, let \(F'\) be its derived subgroup, and, given \(g\in F'\), let \(\text{cl}(g)\) be the commutator length of \(g\). The author describes a new algorithm for calculating the commutator length in free groups. The author also considers some related problems, for example, new upper and lower bounds for \(\text{cl}(g^m)\) are found. Several new problems are posed. Reviewer: E.P.Vdovin (Novosibirsk) Cited in 3 Documents MSC: 20F12 Commutator calculus 20E05 Free nonabelian groups 20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) Keywords:Lie algebras; commutator lengths; growth functions; commutator widths; free groups PDFBibTeX XMLCite \textit{V. G. Bardakov}, Algebra Logika 39, No. 4, 395--440 (2000; Zbl 0960.20019); translation in Algebra Logic 39, No. 4, 224--251 (2000) Full Text: EuDML