All Questions
Tagged with geometric-group-theory nilpotent-groups
8 questions
2
votes
1
answer
203
views
Commensurability classes of subgroups of a nilpotent group
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 ...
- 1,819
5
votes
1
answer
200
views
Example of an invariant metric on a nilpotent group which is not asymptotically geodesic
Let $X$ be a metric space. We say that $X$ is asymptotically geodesic if for all $\epsilon > 0$, there exists $R > 0$ such that, for all $x,y \in X$, there exists some finite sequence of points $...
- 305
5
votes
0
answers
183
views
Finitely generated nilpotent groups as cusp groups
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 $\geq 3$...
- 2,090
1
vote
1
answer
101
views
Relation between flat and nilpotent structures on fibers?
When collapsing Riemannian manifolds under suitable curvature conditions, two types of structure arise on the fibers: flat structures and nilpotent structures. This depends on the scale at which one ...
- 16.6k
11
votes
2
answers
755
views
Quasi-isometric rigidity of Nil
Let $Nil$ be the unique simply connected non-abelian three-dimensional nilpotent Lie group, i.e. the group of upper triangular matrices with all the eigenvalues equal to 1 (this group is also known as ...
- 3,749
2
votes
1
answer
846
views
Word metrics and finite index subgroups
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 ...
- 689
5
votes
0
answers
126
views
Regularity of polynomial growth of groups
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 ...
- 2,449
4
votes
1
answer
855
views
On Canonical generators of torsion free nilpotent group
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 ...
