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

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

• eom: solvable group, Lie group, solvable
• wikipedia solvable group