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### Nilpotent pro-$p$ groups

Is it true that every finitely generated (topologically) torsion free nilpotent pro-$p$ group is isomorphic to a subgroup of $U_d(\mathbb{Z}_p)$, the group of $d\times d$-upper triangular matrices ...

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### Characteristic subgroup of nilpotent group that is not invariant under powering

I want an example of a nilpotent group $G$, a characteristic subgroup $H$, and a prime number $p$ such that:
$G$ is $p$-powered, i.e., every element of $G$ has a unique $p^{th}$ root in $G$.
$H$ is ...

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### 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 ...

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366 views

### Computational complexity of multiplication in a nilpotent group?

What is the computational complexity of multiplication in a Carnot group ?
Background: A Carnot group is a real nilpotent Lie group $N$ whose Lie algebra $Lie(N)$ admits a direct sum decomposition
...

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### Extending a representation to a finite little group

I have a question related to Mackey theory applied to discrete nilpotent groups which are not torsion-free and are infinite.
Let us suppose that $G$ is a type I infinite discrete nilpotent group ...

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100 views

### infranilmanifolds: harmonic forms parallel?

I am studying Lott's paper : "On the spectrum of a finite volume negatively-curved manifold" and the satement is following:
We have an compact infranilmanifold $N$ which is finitely covered by a ...