lower central series

《Abstract Algebra》 · 第 193-194 页 · Section 6.1「p-Groups, Nilpotent Groups, and Solvable Groups」

For any (finite or infinite) group $G$ define the following subgroups inductively: $G^1=[G,G]$ and $G^{i+1}=[G,G^i]$. The chain of groups $G\supseteq G^1\supseteq G^2\supseteq\cdots$ is called the lower central series of $G$.