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

Sources

• 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Chapter $2$: Subgroups and Cosets: $\S 35$
• 1978: John S. Rose: A Course on Group Theory ... (previous) ... (next): $0$: Some Conventions and some Basic Facts