Definition:Non-Trivial Subgroup

Definition
Let $\struct {G, \circ}$ be a group whose identity is $e$.

A non-trivial subgroup of $\struct {G, \circ}$ is a subgroup $\struct {H, \circ}$ of $G$ such that $H \ne \set e$.

Also see

 * Definition:Trivial Subgroup


 * Definition:Trivial Group
 * Definition:Non-Trivial Group