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math.GR2023
The pro-supersolvable topology on a free group: deciding denseness
Claude Marion, Pedro V. Silva, Gareth Tracey
Let be a free group of arbitrary rank and let be a finitely generated subgroup of . Given a pseudovariety of finite groups, i.e. a class of finite groups cl…
math.GR2023
On the closure of cyclic subgroups of a free group in pro-V topologies
Claude Marion, Pedro V. Silva, Gareth Tracey
We determine the closure of a cyclic subgroup of a free group for the pro-{\bf V} topology when {\bf V} is an extension-closed pseudovariety of finite groups. We show that …
math.GR2023★ 1 cited
The pro--solvable topology on a free group
Claude Marion, Pedro V. Silva, Gareth Tracey
We prove that, given a finitely generated subgroup of a free group , the following questions are decidable: is closed (dense) in for the pro-(met)abelian topology? i…