The tag has no wiki summary.

learn more… | top users | synonyms

10
votes
0answers
258 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 ...
9
votes
0answers
235 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 ...
4
votes
0answers
344 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
votes
0answers
77 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 ...