On The Profinite Topology on a Free Group
Copyright policy )On The Profinite Topology on a Free Group
The profinite topology on a free group \(F\) is generated by the subgroups of finite index and their cosets. M. Hall jun. showed that each finitely generated subgroup is closed. J.-E. Pin and the reviewer conjectured that each product \(H_ 1 H_ 2 \dots H_ n\), where each \(H_ i\) is a finitely generated subgroup, is closed. This conjecture is positively answered. The proof uses profinite groups acting on graphs.
- National Academy of Sciences of Belarus Belarus
- Carleton University Canada
- Autonomous University of Madrid Spain
subgroups of finite index, free group, Free nonabelian groups, Subgroup theorems; subgroup growth, Groups acting on trees, profinite groups acting on graphs, Limits, profinite groups, profinite topology, finitely generated subgroup
subgroups of finite index, free group, Free nonabelian groups, Subgroup theorems; subgroup growth, Groups acting on trees, profinite groups acting on graphs, Limits, profinite groups, profinite topology, finitely generated subgroup
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