proper subgroup

A 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 improper subgroup.

Title	proper subgroup
Canonical name	ProperSubgroup
Date of creation	2013-03-22 12:49:10
Last modified on	2013-03-22 12:49:10
Owner	yark (2760)
Last modified by	yark (2760)
Numerical id	7
Author	yark (2760)
Entry type	Definition
Classification	msc 20A99
Related topic	Subgroup
Related topic	Group
Defines	improper subgroup