Rita Gitik, Eliyahu Rips
Abstract
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We present examples of closed subsets of a free group such that their product is not closed in the profinite topology. We discuss how to characterize a subset of a free group which is closed in the profinite topology and its product with any finitely generated subgroup of a free group is also closed in the profinite topology.
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We present examples of closed subsets of a free group such that their product is not closed in the profinite topology. We discuss how to characterize a subset of a free group which is closed in the profinite topology and its product with any finitely generated subgroup of a free group is also closed in the profinite topology.
Key concepts: Profinite group, Free product, Mathematics, Group (periodic table), Product (mathematics), Topology (electrical circuits), Topological group, Finitely-generated abelian group