Improper Subgroup
Return to Glossary.
Formal Definition
If G is a group, then the subgroup consisting of G itself is the improper subgroup of G. All other subgroups are proper subgroups.The subgroup $/{e/}$ is the trivial subgroup of G. All other subgroups are nontrivial.
Informal Definition
An improper subgroup is the subgroup that is the group.
Example(s)
Replace this text with examples
Non-example(s)
Replace this text with non-examples
Additional Comments
Add any other comments you have about the term here