Derived series

Let \(G\) be a group. Set \(G^{(0)} \coloneqq G\) and \(G^{(i+1)} \coloneqq [G^{(i)}, G^{(i)}]\), the commutator subgroup of \(G^{(i)}\), for \(i\geq 0\). The derived series of \(G\) is the chain \(G^{(0)} \geq G^{(1)} \geq G^{(2)} \geq \cdots\).