Potentially characteristic subgroup: Difference between revisions

Latest revision as of 07:00, 22 February 2013

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normal equals potentially characteristic: A normal subgroup $H$ of a group $G$ is potentially characteristic: there exists a group $K$ containing $G$ such that $H$ is a characteristic subgroup of $K$ .
group property-conditionally potentially characteristic subgroup: This is the notion of being potentially characteristic with respect to a group property.
potentially characteristic subgroups characterization problem
potentially operator: This takes as input a subgroup property and outputs the property of being a subgroup that can satisfy the property in some ambient group.

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-* [[NPC theorem]]: A [[normal subgroup]] <math>H</math> of a [[group]] <math>G</math> is potentially characteristic: there exists a group <math>K</math> containing <math>G</math> such that <math>H</math> is a [[characteristic subgroup]] of <math>K</math>.
+* [[normal equals potentially characteristic]]: A [[normal subgroup]] <math>H</math> of a [[group]] <math>G</math> is potentially characteristic: there exists a group <math>K</math> containing <math>G</math> such that <math>H</math> is a [[characteristic subgroup]] of <math>K</math>.
-* [[Group property-conditionally potentially characteristic subgroup]]: This is the notion of being potentially characteristic with respect to a group property.
+* [[group property-conditionally potentially characteristic subgroup]]: This is the notion of being potentially characteristic with respect to a group property.
-* [[potentially characteristic subgroups characterization theorem]]
+* [[potentially characteristic subgroups characterization problem]]
+* [[potentially operator]]: This takes as input a subgroup property and outputs the property of being a subgroup that can satisfy the property in some ambient group.