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Results tagged with nilpotent-groups
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user 174957
6
votes
1
answer
298
views
When is a nilpotent Lie algebra isomorphic to the associated graded of its lower central ser...
All Lie algebras in this question are finite-dimensional and defined over a field $k$ of characteristic $0$ which I'm happy to take to be $\mathbb{R}$ or $\mathbb{C}$.
$\DeclareMathOperator\gr{gr}$Let …
- 437
7
votes
1
answer
307
views
Lower central series vs torsion-free lower central series
$\newcommand\tf{\text{tf}}\newcommand\tor{\text{tor}}$Let $G$ be a finitely generated group. Let $\gamma_k(G)$ denote the $k$th term in the lower central series for $G$, so $\gamma_1(G) = G$ and $\ga …
- 437
6
votes
1
answer
265
views
Betti numbers and lower central series quotients of finite-index subgroups of nilpotent groups
Let $G$ be a finitely generated nilpotent group and let $A\le G$ be a finite-index subgroup. I have two questions about $A$:
Is it true that the inclusion map $A \rightarrow G$ induces isomorphisms …
- 437