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}G 1G 2G k=G,\{ 1\}\subset G_1 \subset G_2 \subset \ldots \subset G_k = G,

in which G j1 is normal in G j and G j/G j1 is abelian.

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