Definition:Non-Trivial Subgroup

Definition
Let $\left({G, \circ}\right)$ be a group whose identity is $e$.

A non-trivial subgroup of $\left({G, \circ}\right)$ is a subgroup $\left({H, \circ}\right)$ of $G$ such that $H \ne \left\{{e}\right\}$.

Also see

 * Definition:Trivial Subgroup


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