Abelian characteristic subgroup: Difference between revisions
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* [[Weaker than::Characteristic central subgroup]] | * [[Weaker than::Characteristic central subgroup]] | ||
* [[Weaker than::Abelian critical subgroup]] | * [[Weaker than::Abelian critical subgroup]] | ||
* [[Weaker than::Maximal among | * [[Weaker than::Maximal among abelian characteristic subgroups]] | ||
===Weaker properties=== | ===Weaker properties=== | ||
Revision as of 22:46, 2 November 2009
This article describes a property that arises as the conjunction of a subgroup property: characteristic subgroup with a group property (itself viewed as a subgroup property): Abelian group
View a complete list of such conjunctions
Definition
Symbol-free definition
A subgroup of a group is termed an Abelian characteristic subgroup if it is Abelian as a group and characteristic as a subgroup.
Examples
VIEW: subgroups satisfying this property | subgroups dissatisfying property characteristic subgroup | subgroups dissatisfying property abelian group
VIEW: Related subgroup property satisfactions | Related subgroup property dissatisfactions
Relation with other properties
Stronger properties
- Cyclic characteristic subgroup
- Characteristic central subgroup
- Abelian critical subgroup
- Maximal among abelian characteristic subgroups