# 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

$\{ 1\}\subset G_1 \subset G_2 \subset \ldots \subset G_k = G,$

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)