I'll try to make it quick. In an exercise, I'm encountering this definition of a nilpotent group:
A group $G$ is nilpotent if there is a finite series of subgroups $\{e\} \subseteq G_n \subseteq G_{n - 1} \subseteq \cdots \subseteq G_0 = G$ with each $G_i \lhd G$ and $G_i/G_{i + 1}$ abelian.
But the definition seems different than any I've seen subsequently, like here. Is this an equivalent definition of a nilpotent group?