supersolvable group SupersolvableGroup 2003-10-04 11:25:53 2004-10-22 17:34:36 Definition supersolvable % this is the default PlanetMath preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them % define commands here A group $G$ is \emph{supersolvable} if it has a finite normal series $$G = G_0 \rhd G_1 \rhd \cdots \rhd G_n = 1$$ with the property that each factor group $G_{i-1}/G_i$ is cyclic. A supersolvable group is solvable. Finitely generated nilpotent groups are supersolvable.