\begin{definition}[Definition:Short Exact Sequence of Groups]
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.
Category:Definitions/Group Theory
\end{definition}