ThmDex – An index of mathematical definitions, results, and conjectures.
▼ Set of symbols
▼ Alphabet
▼ Deduction system
▼ Theory
▼ Zermelo-Fraenkel set theory
▼ Set
▼ Binary cartesian set product
▼ Binary relation
▼ Map
▼ Operation
▼ N-operation
▼ Binary operation
▼ Enclosed binary operation
▼ Groupoid
▼ Semigroup
▼ Monoid
▼ Group
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 $X$