Category:Central Products
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This category contains results about Central Products.
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 $\theta$.
Subcategories
This category has only the following subcategory.
E
- Examples of Central Products (4 P)