Category:Subgroup properties
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
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:
Subcategories
This category has the following 7 subcategories, out of 7 total.
C
Pages in category "Subgroup properties"
The following 200 pages are in this category, out of 728 total. The count includes redirect pages that have been included in the category. Redirect pages are shown in italics.
(previous page) (next page)F
- Finite direct power-closed characteristic subgroup
- Finite elliptic subgroup
- Finite fully invariant subgroup
- Finite injective endomorphism-invariant subgroup
- Finite isomorph-free subgroup
- Finite normal subgroup
- Finite subgroup
- Finite subnormal subgroup
- Finite verbal subgroup
- Finite-automorph-join-closed subnormal subgroup
- Finite-conjugate-join-closed subnormal subgroup
- Finite-dominating subgroup
- Finite-p-potentially characteristic subgroup
- Finite-p-potentially fully invariant subgroup
- Finite-pi-potentially characteristic subgroup
- Finite-pi-potentially fully invariant subgroup
- Finite-pi-potentially verbal subgroup
- Finite-potentially fully invariant subgroup
- Finite-potentially verbal subgroup
- Finitely generated normal subgroup
- Fixed-point subgroup of a subgroup of the automorphism group
- Frattini-embedded normal subgroup
- Free factor
- Free factor of free group
- Free-quotient subgroup
- Frobenius kernel
- Frobenius subgroup
- Fully invariant direct factor
- Fully invariant subgroup
- Fully invariant subgroup of abelian group
- Fully invariant subgroup of finite group
- Fully invariant subgroup of group of prime power order
- Fully invariant subgroup of nilpotent group
- Fully invariant-potentially fully invariant subgroup
- Fully normalized potentially fully invariant subgroup
- Fully normalized subgroup
- Fusion system-relatively strongly closed subgroup
- Fusion system-relatively weakly closed subgroup
H
- Hall direct factor
- Hall retract
- Hall subgroup
- Hall subgroup of normal subgroup
- Hall-relatively weakly closed subgroup
- HEP-subgroup
- Hereditarily 2-subnormal subgroup
- Hereditarily characteristic subgroup
- Hereditarily normal subgroup
- Hereditarily permutable subgroup
- Hereditarily subnormal subgroup
- Homocyclic normal subgroup
- Homocyclic normal subgroup of finite group
- Homomorph-containing subgroup
- Homomorph-containing subgroup of finite group
- Homomorph-dominating subgroup
- Homomorphism-closed subgroup
- Hyperfocal subgroup
- Hypernormalized subgroup
I
- IA-automorphism-balanced subgroup
- IA-automorphism-invariant subgroup
- Image-closed characteristic subgroup
- Image-closed fully invariant subgroup
- Image-closed intermediately subnormal-to-normal subgroup
- Image-potentially fully invariant subgroup
- Improper subgroup
- Index-unique subgroup
- Inert subgroup
- Injective endomorphism-invariant subgroup
- Injective endomorphism-quotient-balanced subgroup
- Intermediately AEP-subgroup
- Intermediately automorph-conjugate subgroup
- Intermediately central factor-to-direct factor
- Intermediately characteristic subgroup
- Intermediately conjugacy-closed-to-retract
- Intermediately endomorphism kernel
- Intermediately fully invariant subgroup
- Intermediately injective endomorphism-invariant subgroup
- Intermediately isomorph-conjugate subgroup
- Intermediately join-transitively subnormal subgroup
- Intermediately local powering-invariant subgroup
- Intermediately normal-to-characteristic subgroup
- Intermediately normal-to-complemented subgroup
- Intermediately normality-large subgroup
- Intermediately powering-invariant subgroup
- Intermediately strictly characteristic subgroup
- Intermediately subnormal-to-normal subgroup
- Intersection of automorph-conjugate subgroups
- Intersection of finitely many intermediately characteristic subgroups
- Intersection of finitely many verbal subgroups
- Intersection of kernels of bihomomorphisms
- Intersection of subnormal subgroups
- Intersection of Sylow subgroups
- Intersection-transitively automorph-conjugate subgroup
- Intersection-transitively central factor
- Intersection-transitively permutable subgroup
- Isomorph-automorphic normal subgroup
- Isomorph-automorphic subgroup
- Isomorph-characteristic subgroup
- Isomorph-commensurable subgroup
- Isomorph-conjugate subgroup
- Isomorph-containing subgroup
- Isomorph-dominating subgroup
- Isomorph-free maximal subgroup of finite group
- Isomorph-free maximal subgroup of group of prime power order
- Isomorph-free subgroup
- Isomorph-free subgroup of finite group
- Isomorph-free subgroup of group of prime power order
- Isomorph-normal characteristic subgroup
- Isomorph-normal characteristic subgroup of group of prime power order
- Isomorph-normal coprime automorphism-invariant subgroup
- Isomorph-normal coprime automorphism-invariant subgroup of group of prime power order
- Isomorph-normal subgroup
- Isomorph-normal subgroup of group of prime power order
- Iterated agemo subgroup of p-group
J
- Join of automorph-conjugate subgroups
- Join of direct factor and central subgroup
- Join of finite normal subgroups
- Join of finitely many 2-subnormal subgroups
- Join of finitely many direct factors
- Join of finitely many pronormal subgroups
- Join of finitely many subnormal subgroups
- Join of homomorph-dominating subgroups
- Join of subnormal subgroups
- Join of Sylow subgroups
- Join-transitively 2-subnormal subgroup
- Join-transitively almost subnormal subgroup
- Join-transitively automorph-conjugate subgroup
- Join-transitively central factor
- Join-transitively finite subgroup
- Join-transitively pronormal subgroup
- Join-transitively subnormal subgroup
L
- Large subgroup
- Lattice automorphism-invariant subgroup
- Lattice-complemented subgroup
- Lattice-isomorph-free subgroup
- Lazard Lie subgroup
- Lazard normal subgroup
- LCS-characteristic subgroup
- LCS-powering-invariant subgroup
- Left residual of intermediately subnormal-to-normal by normal
- Left-quotient-transitively central factor
- Left-transitively 2-subnormal subgroup
- Left-transitively complemented normal subgroup
- Left-transitively fixed-depth subnormal subgroup
- Left-transitively homomorph-containing subgroup
- Left-transitively isomorph-containing subgroup
- Left-transitively permutable subgroup
- Left-transitively WNSCDIN-subgroup
- Linear-bound join-transitively subnormal subgroup
- Local divisibility-closed subgroup
- Local powering-invariant normal subgroup
- Local powering-invariant normal subgroup of nilpotent group
- Local powering-invariant subgroup
- Local subgroup
- Local subgroup for a prime
- Locally inner automorphism-balanced subgroup
- Locally nilpotent normal subgroup
- Locally subnormal subgroup
M
- Malnormal subgroup
- Marginal subgroup
- Marginal subgroup of finite type
- Max-core
- Max-sensitive subgroup
- Maximal among abelian characteristic subgroups
- Maximal among abelian normal subgroups
- Maximal among abelian subgroups
- Maximal among abelian subgroups of maximum rank
- Maximal subgroup
- Maximal subgroup of finite nilpotent group
- Maximal subgroup of group of prime power order
- Maximal subgroup of Sylow subgroup
- Maximal Sylow intersection
- Meet-irreducible subgroup
- Minimal characteristic subgroup
- Minimal CL-subgroup
- Minimal normal subgroup
- Modular 2-subnormal subgroup
- Modular subgroup
- Modular subnormal subgroup
- Monadic second-order characteristic subgroup
- MWNSCDIN-subgroup
N
- NE-subgroup
- Nearly closed subgroup
- Nearly normal subgroup
- Nilpotent characteristic subgroup
- Nilpotent Hall subgroup
- Nilpotent normal subgroup
- Nilpotent pronormal subgroup
- Nilpotent quotient-by-core subgroup
- Nilpotent subnormal subgroup
- Nilpotent-quotient subgroup
- Nontrivial subgroup
- Normal abelian subgroup
- Normal AEP-subgroup
- Normal closure of finite subset
- Normal fully normalized subgroup
- Normal Hall subgroup
- Normal intermediately AEP-subgroup