Category:Subgroup property conjunctions
From Groupprops
This category lists subgroup properties obtaind as the conjunction (AND) of two or more subgroup properties, that are considered more fundamental or important
Pages in category "Subgroup property conjunctions"
The following 200 pages are in this category, out of 210 total. The count includes redirect pages that have been included in the category. Redirect pages are shown in italics.
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- Abelian characteristic subgroup
- Abelian conjugacy-closed subgroup
- Abelian critical subgroup
- Abelian direct factor
- Abelian fully invariant subgroup
- Abelian hereditarily normal subgroup
- Abelian marginal subgroup
- Abelian normal subgroup
- Abelian normal subgroup of group of prime power order
- Abelian pronormal subgroup
- Abelian subgroup of maximum order which is normal
- Abelian subnormal subgroup
- Abelian Sylow subgroup
- Abelian verbal subgroup
- Automorphism-faithful AEP-subgroup
- Automorphism-faithful normal subgroup
C
- C-closed normal subgroup
- C-closed self-centralizing subgroup
- Center-fixing automorphism-balanced subgroup
- Central subgroup
- Central subgroup of finite group
- Central subgroup of normalizer
- Centralizer-free normal subgroup
- Centralizer-free subgroup
- Characteristic AEP-subgroup
- Characteristic central factor
- Characteristic central subgroup
- Characteristic direct factor
- Characteristic direct factor of abelian group
- Characteristic direct factor of nilpotent group
- Characteristic maximal subgroup of group of prime power order
- Characteristic subgroup of abelian group
- Characteristic subgroup of finite group
- Characteristic subgroup of finite index
- Characteristic subgroup of group of prime power order
- Characteristic subgroup of nilpotent group
- Characteristic subgroup of solvable group
- Characteristic transitively normal subgroup
- Characteristically complemented characteristic subgroup
- Class two characteristic subgroup
- Class two normal subgroup
- Commutator-in-center subgroup
- Complemented central factor
- Complemented characteristic subgroup
- Complemented fully invariant subgroup
- Complemented homomorph-containing subgroup
- Complemented isomorph-containing subgroup
- Complemented transitively normal subgroup
- Complete characteristic subgroup
- Complete direct factor
- Completely divisibility-closed normal subgroup
- Component
- Conjugacy-closed characteristic subgroup
- Conjugacy-closed Hall subgroup
- Conjugacy-closed normal subgroup
- Coprime automorphism-faithful characteristic subgroup
- Coprime automorphism-faithful normal subgroup
- Coprime automorphism-invariant normal subgroup
- Coprime automorphism-invariant normal subgroup of group of prime power order
- Coprime automorphism-invariant subgroup of group of prime power order
- Core-free 2-subnormal subgroup
- Core-free permutable subgroup
- Core-free subnormal subgroup
- Cyclic characteristic subgroup
- Cyclic isomorph-containing subgroup
- Cyclic normal subgroup
D
F
- Finite 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
- Finitely generated normal subgroup
- Free factor of free group
- Fully invariant direct factor
- Fully invariant subgroup of abelian group
- Fully invariant subgroup of finite group
- Fully invariant subgroup of nilpotent group
- Fully normalized potentially fully invariant subgroup
H
I
- Isomorph-automorphic normal 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 of group of prime power order
L
M
N
- Nilpotent characteristic subgroup
- Nilpotent Hall subgroup
- Nilpotent normal subgroup
- Nilpotent pronormal subgroup
- Nilpotent subnormal subgroup
- Normal AEP-subgroup
- Normal fully normalized subgroup
- Normal Hall subgroup
- Normal intermediately AEP-subgroup
- Normal subgroup contained in centralizer of derived subgroup
- Normal subgroup having a 1-closed transversal
- Normal subgroup in which every subgroup characteristic in the whole group is characteristic
- Normal subgroup of finite group
- Normal subgroup of finite index
- Normal subgroup of finitely generated group
- Normal subgroup of group of prime power order
- Normal subgroup of nilpotent group
- Normal subgroup of periodic group
- Normal subgroup of prime index
- Normal subgroup of prime order
- Normal subgroup whose automorphism group is abelian
- Normal subgroup whose center is contained in the center of the whole group
- Normal subgroup whose derived subgroup equals its intersection with whole derived subgroup
- Normal subgroup whose focal subgroup equals its derived subgroup
- Normal subgroup whose inner automorphism group is central in automorphism group
- Normal Sylow subgroup
- Normality-large normal subgroup
O
P
- P-automorphism-invariant subgroup of finite p-group
- P-core-automorphism-invariant subgroup of finite p-group
- Perfect 2-subnormal subgroup
- Perfect characteristic subgroup
- Perfect direct factor
- Perfect normal subgroup
- Perfect subnormal subgroup
- Periodic normal subgroup
- Periodic subgroup
- Permutable 2-subnormal subgroup
- Permutable subnormal subgroup
- Permutably complemented Hall subgroup
- Powering-invariant central subgroup
- Powering-invariant characteristic subgroup
- Powering-invariant characteristic subgroup of nilpotent group
- Powering-invariant normal subgroup
- Powering-invariant normal subgroup of nilpotent group
- Powering-invariant subgroup of abelian group
- Powering-invariant subgroup of nilpotent group
- Prehomomorph-contained subgroup of finite group
- Pronormal Hall subgroup
- Proper characteristic subgroup
- Proper normal subgroup
- Pure subgroup of torsion-free abelian group
R
S
- Self-centralizing direct factor
- Self-centralizing normal subgroup
- Self-normalizing Sylow subgroup
- Simple normal subgroup
- Simple subnormal subgroup
- Solvable characteristic subgroup
- Solvable normal subgroup
- Subgroup of abelian group
- Subgroup of finite abelian group
- Subgroup of finite cyclic group
- Subgroup of finite group
- Subgroup of finite index in finitely generated group
- Subgroup of finite nilpotent group
- Subgroup of finite solvable group
- Subgroup of free group
- Subgroup of nilpotent group
- Subgroup of solvable group
- Subgroup whose normalizer equals its normal closure
- Subnormal subgroup of finite group
- Subnormal subgroup of finite index
- Subnormal-permutable subnormal subgroup
- Sylow direct factor
- Sylow retract
