Definition:Short Exact Sequence of Groups

Definition
Let $(G,\cdot)$ 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.