Open subgroups of free topological groups

Jeremy Brazas

Fundamenta Mathematicae (2014)

  • Volume: 226, Issue: 1, page 17-40
  • ISSN: 0016-2736

Abstract

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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.

How to cite

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Jeremy Brazas. "Open subgroups of free topological groups." Fundamenta Mathematicae 226.1 (2014): 17-40. <http://eudml.org/doc/282798>.

@article{JeremyBrazas2014,
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.},
author = {Jeremy Brazas},
journal = {Fundamenta Mathematicae},
keywords = {free topological group; topological fundamental group; semicovering map},
language = {eng},
number = {1},
pages = {17-40},
title = {Open subgroups of free topological groups},
url = {http://eudml.org/doc/282798},
volume = {226},
year = {2014},
}

TY - JOUR
AU - Jeremy Brazas
TI - Open subgroups of free topological groups
JO - Fundamenta Mathematicae
PY - 2014
VL - 226
IS - 1
SP - 17
EP - 40
AB - 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.
LA - eng
KW - free topological group; topological fundamental group; semicovering map
UR - http://eudml.org/doc/282798
ER -

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