Definition:Extension Problem

Definition

Let $H$ and $K$ be groups.

The extension problem is to determine all groups $G$ such that:

$K \trianglelefteq G$

$G / K \cong H$

where:

$K \trianglelefteq G$ denotes that $K$ is a normal subgroup of $G$

$G / K$ denotes the quotient group of $G$ by $K$

$\cong$ denotes group isomorphism.

Sources

• 1978: John S. Rose: A Course on Group Theory ... (previous) ... (next): $1$: Introduction to Finite Group Theory: $1.7$