# proper subgroup

A proper subgroup of a group $G$ is a subgroup $H$ of $G$ such that $H\neq G$.

The only subgroup of $G$ that is not a proper subgroup is $G$ itself, which may therefore occasionally be called an improper subgroup.

Title proper subgroup ProperSubgroup 2013-03-22 12:49:10 2013-03-22 12:49:10 yark (2760) yark (2760) 7 yark (2760) Definition msc 20A99 Subgroup Group improper subgroup