Normal closure-finding problem

This article describes the subgroup operator computation problem for the subgroup operator: normal closure

Description

We are given a group $G$ and a subgroup $H$ specified by some means (typically using generating sets, though we may also specify them using membership tests). The goal is to obtain a description of the normal closure $K=H^G$ of $H$ in $G$ using the same language (so if $G$ and $H$ are described using generating sets, we want a generating set for $K$, whereas if $G$ and $H$ are described using membership tests, then $K$ is also to be described using a membership test.

Relation with other problems

Problems it reduces to

• Normality testing problem: See black-box reduction of normal closure-finding in terms of generating sets to normality testing.