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math.GR2021
Constructing uncountably many groups with the same profinite completion
Nikolay Nikolov, Dan Segal
We present two uncountable families of finitely generated residually finite groups all having the same profinite completion. One consists of soluble groups, the other of branch gro…
math.GR2021
Torsion growth in finitely presented pro- groups
Nikolay Nikolov
We prove that torsion in the abelianizations of open normal subgroups in finitely presented pro- groups can grow arbitrarily fast. By way of contrast in - analytic…
math.GR2021
On profinite groups with positive rank gradient
Nikolay Nikolov
We prove that a profinite group with positive rank gradient does not satisfy a group law. In the case when is a pro- group we show that contains a nonabelian dense f…