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
▼ Action
▼ Group action
▼ Group action space
▼ Stabiliser
▼ Translation stabiliser
▼ Conjugation stabiliser
▼ Left conjugation stabiliser
▼ Centraliser
Definition D1563
Group centre
Formulation 1
Let $G$ be a D22: Group such that
(i) $H$ is a D496: Subgroup of $G$
The centre in $G$ modulo $H$ is the D11: Set \begin{equation} Z(H) : = \{ h \in H \mid \forall \, g \in G : h g h^{-1} = g \} \end{equation}
Results
▶ R756: Abelian group iff centre is whole group
▶ R755: Group centre is Abelian group