Category:Subgroup properties
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This is a monster category, that is, it has a lot of members. Please use the subcategory structure of this category or other tools (Such as lookup and exploration guideline pages) to explore the category more effectively
This is a category of properties for the following kind of objects: subgroups. In other words, this category lists subgroup properties
All articles in subcategories of this category are also directly included in this category
View a complete list of property categories
This is the category of important instances of subgroup property. Please check the:
The inclusion template for this category is Template:Subgroup property. Note that inclusion in any subcategory may or may not guarantee direct inclusion into the given category.
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Related categories
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 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
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Subcategories
This category has the following 2 subcategories, out of 6 total.
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Pages in category "Subgroup properties"
The following 198 pages are in this category, out of 627 total. The count includes redirect pages that have been included in the category. Redirect pages are shown in italics.
