Normal closure-finding problem: Difference between revisions

Latest revision as of 20:48, 25 June 2013

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

The normal closure-finding problem is the general name for a class of problems where a group $G$ is described using a group description rule, a subgroup $H$ is described using a subgroup description rule, and our goal is to use a (specified) subgroup description rule to find the normal closure $H^{G}$ .

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 ==Description==
-We are given a [[group]] <math>G</math> specified via an [[encoding of a group|encoding]] (or [[quasi-encoding of a group|quasi-encoding]] or [[multi-encoding of a group|multi-encoding]]) and a [[subgroup]] <math>H</math> 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]] <math>K = H^G</math> of <math>H</math> in <math>G</matH> by some means (which may be using generating sets or membership tests or both).
+The '''normal closure-finding problem''' is the general name for a class of problems where a group <math>G</math> is described using a [[group description rule]], a [[subgroup]] <math>H</math> is described using a [[subgroup description rule]], and our goal is to use a (specified) [[subgroup description rule]] to find the [[normal closure]] <math>H^G</math>.
 ==Relation with other problems==