Year: 2022
Type: article
Abstract: Let G be the first Grigorchuk group. We show that the commutator width of G is 2 : every element g\in [G,G] is a product of two commutators, and also of six conjugates of a . Furthermore, we show that every finitely generated subgroup H\leq 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.
Source: Groups Geometry and Dynamics
DOI: 10.4171/ggd/666
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W2765446779