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 a generating set, though we may also specify it using a membership test). The goal is to obtain a description of the normal closure $K=H^G$ of $H$ in $G$ by some means (which may be using generating sets or membership tests or both).

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.