Category:Subgroup properties

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This is a category of properties for the following kind of objects: subgroups. In other words, this category lists subgroup properties
View a complete list of property categories

Important group properties, sorted by importance rank:

Extremely important (importance rank one):
 Defining ingredient
Characteristic subgroupCharacteristic subalgebra
Direct factorInternal direct product
Normal subgroup
Normal complement
Retract
Improper subgroup
Maximal subgroupMaximal operator
Proper subgroup
Nontrivial subgroupTrivial group
Normal subgroupHomomorphism of groups
Inner automorphism
Conjugate subgroups
Left coset of a subgroup
Right coset of a subgroup
Conjugacy class
Commutator of two subgroups
Proper characteristic subgroupProper subgroup
Characteristic subgroup
Proper normal subgroupProper subgroup
Normal subgroup
Proper subgroup
Very important (importance rank two):
 Defining ingredient
Central factorInner automorphism
Centralizer
Normal subgroup
Quotient group maps to outer automorphism group of normal subgroup
Internal central product
Image-potentially operator
Direct factor
Upper join-closure operator
Cocentral subgroup
Central subgroupCentral factor
Abelian group
Complemented normal subgroup
Fully invariant subgroupEndomorphism of a group
Hall subgroup
Normal Hall subgroupNormal subgroup
Hall subgroup
Subnormal subgroup
Characteristic subgroup
Normal Sylow subgroupNormal subgroup
Sylow subgroup
Finite group
Subnormal subgroup
Characteristic subgroup
Fully invariant subgroup
Retract
Subnormal subgroupNormal subgroup
Subordination operator
Sylow subgroupGroup of prime power order
Index of a subgroup
Order of a group
Hall subgroup
Somewhat important (importance rank three):
 Defining ingredient
Automorph-conjugate subgroupAutomorphic subgroups
Conjugate subgroups
Normal subgroup
Normalizer of a subgroup
Permutable subgroupProduct of subgroups
Permuting subgroups
Pronormal subgroupConjugate subgroups
Join of subgroups

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:

Testing/computational problems

Facts and proofs related to subgroup properties

Notations page

The page giving notations for important subgroup properties is:

Notation for subgroup properties

Pages in category "Subgroup properties"

The following 200 pages are in this category, out of 729 total. The count includes redirect pages that have been included in the category. Redirect pages are shown in italics.

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