Geodesic
Commutator length of abelian-by-nilpotent groups
Glasgow mathematical journal, Tome 40 (1998) no. 1, pp. 117-121

Voir la notice de l'article provenant de la source Cambridge University Press

Let G be a group and C = [G, G] be its commutator subgroup. Denote by c(G) the minimal number such that every element of G′ can be expressed as a product of at most c(G) commutators. The exact values of c{G) are computed when G is a free nilpotent group or a free abelian-by-nilpotent group. If G is a free nilpotent group of rank n>2 and class c>2, c(G) = [n/2] if c = 2 and c(G) = n if c>2. If G is a free abelian-by-nilpotent group of rank n > 2 then c(G) = n. 
Akhavan-Malayeri, Mehri; Rhemtulla, Akbar. Commutator length of abelian-by-nilpotent groups. Glasgow mathematical journal, Tome 40 (1998) no. 1, pp. 117-121. doi: 10.1017/S0017089500032407
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