Category:Subgroup properties

Important group properties, sorted by importance rank:

Extremely important (importance rank one): Very important (importance rank two): Somewhat important (importance rank three):

Subcategory for pivotal elements
To see only the more important, or pivotal, among subgroup properties, refer Category:Pivotal subgroup properties.

Properties/metaproperties
Related categories include:


 * Category:Properties of subsets of groups
 * Category:Subgroup pair properties
 * Category:Properties of subgroup series
 * Category:Properties of subgroup families
 * Category:Subgroup metaproperties

Testing/computational problems

 * Category:Subgroup property testing problems

Facts and proofs related to subgroup properties

 * Category:Subgroup property implications is a list of articles, each article describing an implication between two subgroup properties. For instance, characteristic implies normal meaning that every characteristic subgroup is a normal subgroup.
 * Category:Subgroup property non-implications is a list of articles, each article describing why a particular subgroup property does not imply another one. Usually, the proof is constructive, giving an example of a subgroup satisfying the second property but not the first. For instance, normal not implies characteristic
 * Category:Subgroup metaproperty satisfactions is a list of articles, each article describing how/why a given subgroup property satisfies a given subgroup metaproperty.
 * Category:Subgroup metaproperty dissatisfactions is a list of articles, each article describing how/why a given subgroup property does not satisfy a given subgroup metaproperty.

Notations page
The page giving notations for important subgroup properties is:

Notation for subgroup properties