Normal closure-finding problem

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

Description

Given data

Our universe is some group $U$ specified by means of an encoding.

A group $G$ in $U$ is specified by a generating set $A$, and a subgroup $H$ of $G$ is specified by a generating set $B$. (We are given a guarantee that $H$ is a subgroup of $G$, if not, we can test it using the algorithm for the subgroup testing problem).

Goal

Let $K$ be the normal closure of $H$ in $G$. We are required to determine a generating set $C$ for $K$.

Relation with other problems

Problems it reduces to

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