Open subgroups of free topological groups
Algebraic Topology
2014-06-17 v2 General Topology
Abstract
The theory of covering spaces is often used to prove the Nielsen-Schreier theorem, which states that every subgroup of a free group is free. We apply the more general theory of semicovering spaces to obtain analogous subgroup theorems for topological groups: Every open subgroup of a free Graev topological group is a free Graev topological group. An open subgroup of a free Markov topological group is a free Markov topological group if and only if it is disconnected.
Cite
@article{arxiv.1209.5486,
title = {Open subgroups of free topological groups},
author = {Jeremy Brazas},
journal= {arXiv preprint arXiv:1209.5486},
year = {2014}
}
Comments
19 pages, 1 figure