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==
-===Given data===
+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>.
-Our universe is some group <math>U</math> specified by means of an [[encoding]].
-A group <math>G</math> in <math>U</math> is specified by a generating set <math>A</math>, and a subgroup <math>H</math> of <math>G</math> is specified by a generating set <math>B</math>. (We are given a guarantee that <math>H</math> is a subgroup of <math>G</math>, if not, we can test it using the algorithm for the [[subgroup testing problem]]).
-===Goal===
-Let <math>K</math> be the [[normal closure]] of <math>H</math> in <math>G</math>. We are required to determine a generating set <math>C</math> for <math>K</math>.
 ==Relation with other problems==
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 ===Problems it reduces to===
-* [[Normality testing problem]]: See [[black-box reduction of normal closure-finding to normality testing]].
+* [[Normality testing problem]]: See [[black-box reduction of normal closure-finding in terms of generating sets to normality testing]].