Definition:Short Exact Sequence of Groups

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Definition

Let $\left({G, \cdot}\right)$ be a group.

An exact sequence of the form

$1 \longrightarrow K \stackrel{\alpha}{\longrightarrow} G \stackrel{\beta}{\longrightarrow} H \longrightarrow 1$

is called a short exact sequence, where $1$ represents the trivial group.