All Questions

I recently learned about the following question, asked by I. Kapovich : Is there an example of a group $G$ which is hyperbolic relative to some parabolic subgroups that are nilpotent of class $\geq 3$...

Let $G$ be a finitely generated group of polynomial growth. This means that the size $B_n$ of the ball of radius $n$ satsifies: $$ A n^d \leq B_n \leq Bn^d $$ for some constants $A$, $B$. My question ...

I read somewhere that Maltcev proved that for any finitely generated torsion free Nilpotent group $G$ there are canonical generators, i.e. $g_{1},\ldots,g_{k}$ such that any $g \in G$ can be written ...

Here is a question I stumbled upon in my research. Question: Given a finitely generated nilpotent group $G$, do its subgroups fall into finitely many abstract commensurability classes? Recall that two ...

Suppose that we are given some finitely generated group $ G $ and some finite index subgroup of it $ H $. Given a finite generating symmetric generating set $ S \subset G $, we can define the word ...