Commutator width in the first Grigorchuk group

10/16/2017

∙

by   Laurent Bartholdi, et al.

∙

0

∙

share

Let G be the first Grigorchuk group. We show that the commutator width of G is 2: every element g∈ [G,G] is a product of two commutators, and also of six conjugates of a. Furthermore, we show that every finitely generated subgroup H≤ G has finite commutator width, which however can be arbitrarily large, and that G contains a subgroup of infinite commutator width. The proofs were assisted by the computer algebra system GAP.