Image-closed characteristic subgroup: Difference between revisions
No edit summary |
|||
| Line 11: | Line 11: | ||
A [[subgroup]] <math>H</math> of a [[group]] <math>G</math> is termed '''image-closed characteristic''' in <math>G</math> if, for any normal subgroup <math>N</math> of <math>G</math>, <math>HN/N</math> is a characteristic subgroup of <math>G/N</math>. | A [[subgroup]] <math>H</math> of a [[group]] <math>G</math> is termed '''image-closed characteristic''' in <math>G</math> if, for any normal subgroup <math>N</math> of <math>G</math>, <math>HN/N</math> is a characteristic subgroup of <math>G/N</math>. | ||
==Formalisms== | |||
{{obtainedbyapplyingthe|image condition operator|characteristic subgroup}} | |||
==Relation with other properties== | ==Relation with other properties== | ||
Revision as of 13:47, 26 May 2009
BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]
Definition
Symbol-free definition
A subgroup of a group is termed an image-closed characteristic subgroup if, under any surjective homomorphism, its image is a characteristic subgroup of the image.
Definition with symbols
A subgroup of a group is termed image-closed characteristic in if, for any normal subgroup of , is a characteristic subgroup of .
Formalisms
In terms of the image condition operator
This property is obtained by applying the image condition operator to the property: characteristic subgroup
View other properties obtained by applying the image condition operator