The nilpotent-groups tag has no usage guidance.

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362 views

### 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 ...

**11**

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307 views

### 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 ...

**5**

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184 views

### Reconstructing a nilpotent Lie algebra from its cohomology with $A_{\infty}$-structure

Let $L$ be a nilpotent Lie algebra (over a field of char 0) and $CE^{\bullet}(L)$ be its Chevalley-Eilenberg dg-algebra. By homotopy transfer, there exists a structure of an $A_{\infty}$-algebra on ...

**4**

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108 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 ...

**4**

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599 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
...

**2**

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97 views

### 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 ...

**1**

vote

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75 views

### Lower central series in a free pro-p group

Let $F$ be a nonabelian finitely generated free pro-$p$ group, $H \leq_c F$ of infinite index. Denote by $\{F_n\}_{n \in \mathbb{N}}$ the lower central series of $F$, and set $r_n = [F : F_nH]$.
Is ...

**1**

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152 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 ...

**0**

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10 views

### Does Weil-Brezin transform provide Fourier basis in C^0 on Heisenberg manifold?

I know that $L^2$ functions of the Heisenberg nilmanifold are spanned by images of the Weil-Brezin transform. Is it true that they are also dense in C^0? Is there a reference for this?

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124 views

### A normal form theorem for presentations of finite $p$-groups of nilpotency class $2$?

When constructing examples of nonabelian finite $p$-groups with abelian automorphism group (and certain other desired properties), the authors of papers like http://arxiv.org/pdf/1304.1974v1.pdf leave ...