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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.

MSC:

20F12 Commutator calculus
20E05 Free nonabelian groups
20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects)
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