On Closed Subsets of Free Groups
Rita Gitik, Eliyahu Rips
TL;DR
This paper provides examples of finitely generated subgroups and subsets in free groups that are closed in the profinite topology, but their product is not, highlighting complexities in the topological structure of free groups.
Contribution
It presents the first known examples demonstrating that the product of two closed subsets in a free group need not be closed in the profinite topology.
Findings
Existence of finitely generated subgroups with non-closed products
Existence of closed subsets with non-closed products
Insights into the topological properties of free groups
Abstract
We give two examples of a finitely generated subgroup of a free group and a subset, closed in the profinite topology of a free group, such that their product is not closed in the profinite topology of a free group.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Topology and Set Theory · Finite Group Theory Research