# nLab solvable group

A group is solvable if it is a finite iterated extension of an abelian group by abelian groups. In other words, there exists a finite sequence

$\left\{1\right\}\subset {G}_{1}\subset {G}_{2}\subset \dots \subset {G}_{k}=G,$\{ 1\}\subset G_1 \subset G_2 \subset \ldots \subset G_k = G,

in which ${G}_{j-1}$ is normal in ${G}_{j}$ and ${G}_{j}/{G}_{j-1}$ is abelian.

Created on June 16, 2011 17:51:04 by Zoran Škoda (161.53.130.104)