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

Résumé

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.

Détail

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