67 citations · 528 across the 47 of their papers we have counts for
32 papers · 1 filter
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…
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…
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…
2D problems in groups
Aditi Kar, Nikolay Nikolov
We investigate a conjecture about stabilisation of deficiency in finite index subgroups and relate it to the D2 Problem of C.T.C. Wall and the Relation Gap problem. We verify the p…
Some remarks on finitarily approximable groups
Nikolay Nikolov, Jakob Schneider, Andreas Thom
The concept of a C-approximable group, for a class of finite groups C, is a common generalization of the concepts of a sofic, weakly sofic, and linear sofic group. Glebsky raised t…
Growth of homology torsion of metabelian groups
Nikolay Nikolov
We study the growth of torsion in the abelianizations of finite index subgroups in finitely generated metabelian groups. This complements earlier work of Kar, Kropholler and the au…