Composition series

Let \(G\) be a group with identity \(e\). A composition series of \(G\) is a finite normal series \[ G = G^0 \geq G^1 \geq \cdots \geq G^n = \theset{e}, \qquad G^{i+1}\normal G^i, \] such that for each \(0\leq i<n\), \(G^{i+1}\) is a maximal proper normal subgroup of \(G^i\).