proper subgroup ProperSubgroup 2002-06-27 19:44:33 2006-10-28 11:36:54 Definition improper subgroup \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} A \emph{proper subgroup} of a group $G$ is a subgroup $H$ of $G$ such that $H\ne G$. The only subgroup of $G$ that is not a proper subgroup is $G$ itself, which may therefore occasionally be called an \emph{improper subgroup}.