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

Akhavan-Malayeri, Mehri

Bull. Korean Math. Soc. 43, No. 4, 805-812 (2006).

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.

Reviewer: V. A. Roman’kov (Omsk)

MSC:

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

Keywords:

maximal condition; products of commutators; finitely generated solvable groups; derived lengths; numbers of commutators