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arXiv · 1209.5486

Open subgroups of free topological groups

Jeremy Brazas
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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.

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Jeremy Brazas. 2013-02-01. Open subgroups of free topological groups. https://arxiv.org/abs/1209.5486

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