Open subgroups of free topological groups

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.

19 pages, 1 figure

References in corpus (1)

• The fundamental group as a topological group

Cited by in corpus (1)

• On fundamental groups with the quotient topology