Lower central series

Let \(G\) be a group. Set \(G^0 \coloneqq G\) and \(G^{i+1} \coloneqq [G, G^i]\) for \(i\geq 0\), where \([G, G^i]\) is the subgroup generated by the commutators \(ghg^{-1}h^{-1}\) with \(g\in G\) and \(h\in G^i\). The lower central series of \(G\) is the chain \(G^0 \geq G^1 \geq \cdots\).