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
Abelian group iff centre is whole group
Group centre is Abelian group