# Definition:Trivial Subgroup

## Definition

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

Then the algebraic structure $\struct {\set e, \circ}$ is called the trivial subgroup of $\struct {G, \circ}$.

## Also denoted as

Some authors use $e$ to refer to both the identity and the trivial subgroup $\set e$.