Commutator length of solvable groups satisfying max-\(n\). (English) Zbl 1129.20023

Let \(G\) be a group and \(G'\) be its derived subgroup. Let \(c(G)\) denote the width of \(G'\) as verbal subgroup with respect to the standard commutator word \(w=[x,y]\). In other words, let \(c(G)\) be the minimal possible number (or \(\infty\)) such that every element \(g\in G'\) can be presented as a product of \(c(G)\) commutators.
The author gives a suitable bound for \(c(G)\) when \(G\) is a finitely generated solvable group of derived length \(r\) satisfying the maximal condition for normal subgroups.


20F12 Commutator calculus
20F16 Solvable groups, supersolvable groups
20F05 Generators, relations, and presentations of groups
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