# Category:Pullbacks of Quotient Group Isomorphisms

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This category contains results about **Pullbacks of Quotient Group Isomorphisms**.

Let $G, H$ be groups.

Let $N \lhd G, K \lhd H$ be normal subgroups of $G$ and $H$ respectively.

Let:

- $G / N \cong H / K$

where:

- $G / N$ denotes the quotient of $G$ by $N$
- $\cong$ denotes group isomorphism.

Let $\theta: G / N \to H / K$ be such a group isomorphism.

The **pullback $G \times^\theta H$ of $G$ and $H$ via $\theta$** is the subset of $G \times H$ of elements of the form $\tuple {g, h}$ where $\map \theta {g N} = h K$.

## Subcategories

This category has only the following subcategory.

## Pages in category "Pullbacks of Quotient Group Isomorphisms"

This category contains only the following page.