On double cosets in free groups
Rita Gitik, Eliyahu Rips
TL;DR
This paper proves that for any finitely generated subgroups H and K of a free group F, and any element g in F, the double coset HgK is closed in the profinite topology of F, advancing understanding of subgroup structures.
Contribution
It establishes the closure of double cosets in the profinite topology for finitely generated subgroups in free groups, a novel result in group topology.
Findings
Double cosets are closed in the profinite topology.
Finitely generated subgroups have specific topological properties.
Enhances understanding of free group subgroup structures.
Abstract
It is shown that for any finitely generated subgroups H and K of a free group F, and for any element g in F the double coset HgK is closed in the profinite topology of F.
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Taxonomy
TopicsGeometric and Algebraic Topology