**trivial group**if and only if

(1) | $X$ is a D135: Singleton set |

(2) | $f$ is a D4428: Canonical identity map on $X$ |

Definition D1240

Trivial group

Formulation 0

An D548: Ordered pair $G = (X, f)$ is a **trivial group** if and only if

(1) | $X$ is a D135: Singleton set |

(2) | $f$ is a D4428: Canonical identity map on $X$ |