Category:Examples of Central Products

This category contains examples of Central Product.

Let $G$ and $H$ be groups.

Let $Z$ and $W$ be central subgroups of $G$ and $H$ respectively.

Let:

$Z \cong W$

where $\cong$ denotes isomorphism.

Let such a group isomorphism be $\theta: Z \to W$.

Let $X$ be the set defined as:

$X = \set {\tuple {x, \map \theta x^{-1} }: x \in Z}$

Then the quotient group $\struct {G \times H} / X$ is denoted $\struct {G \times_\theta H}$ and is called the central product of $G$ and $H$ via $\theta$.