Geodesic
Open subgroups of free topological groups
Jeremy Brazas1
1 Department of Mathematics and Statistics Georgia State University Atlanta, GA 30303, U.S.A.
Fundamenta Mathematicae, Tome 226 (2014) no. 1, pp. 17-40.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/fm226-1-2
Keywords: theory covering spaces often prove nielsen schreier theorem which states every subgroup group apply general theory semicovering spaces obtain analogous subgroup theorems topological groups every subgroup graev topological group graev topological group subgroup markov topological group markov topological group only disconnected

Jeremy Brazas 1

1 Department of Mathematics and Statistics Georgia State University Atlanta, GA 30303, U.S.A. 
@article{10_4064_fm226_1_2,
     author = {Jeremy Brazas},
     title = {Open subgroups of free topological groups},
     journal = {Fundamenta Mathematicae},
     pages = {17--40},
     publisher = {mathdoc},
     volume = {226},
     number = {1},
     year = {2014},
     doi = {10.4064/fm226-1-2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/fm226-1-2/}
}
TY  - JOUR
AU  - Jeremy Brazas
TI  - Open subgroups of free topological groups
JO  - Fundamenta Mathematicae
PY  - 2014
SP  - 17
EP  - 40
VL  - 226
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/fm226-1-2/
DO  - 10.4064/fm226-1-2
LA  - en
ID  - 10_4064_fm226_1_2
ER  - 
%0 Journal Article
%A Jeremy Brazas
%T Open subgroups of free topological groups
%J Fundamenta Mathematicae
%D 2014
%P 17-40
%V 226
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/fm226-1-2/
%R 10.4064/fm226-1-2
%G en
%F 10_4064_fm226_1_2
Jeremy Brazas. Open subgroups of free topological groups. Fundamenta Mathematicae, Tome 226 (2014) no. 1, pp. 17-40. doi : 10.4064/fm226-1-2. http://geodesic.mathdoc.fr/articles/10.4064/fm226-1-2/

Cité par Sources :