Lower central series
= Lower central series
{title2=$\gamma_i(G)$}
{wiki}
The lower central series of a group is defined by $\gamma_1(G)=G$ and $\gamma_{i+1}(G)=[\gamma_i(G),G]$. A group is nilpotent of class at most $c$ exactly when $\gamma_{c+1}(G)$ is trivial.