Free groups, covering spaces and Artin's theorem
History and Overview
2019-05-15 v4 Algebraic Topology
Abstract
In this expository note we provide a proof of Artin's theorem which states that the commutator subgroup of a free group on two generators is not finitely generated. The proof employs the infinite grid as in two other proofs in the literature mentioned in the note but takes a somewhat different approach which seems to be of didactic value.
Keywords
Cite
@article{arxiv.1904.07689,
title = {Free groups, covering spaces and Artin's theorem},
author = {Gopala Krishna Srinivasan},
journal= {arXiv preprint arXiv:1904.07689},
year = {2019}
}