Solvable group

Let \(G\) be a group with identity \(e\). The group \(G\) is solvable if there is a finite normal series \[ \theset{e} = G_0 \normal G_1 \normal \cdots \normal G_n = G \] such that \(G_{i}/G_{i-1}\) is abelian for every \(1\leq i\leq n\).