Property:Stronger than

From Groupprops

The stronger than attribute is used to compare two elements in a partially ordered set. Typically, it is used to compare two (yes/no type) properties. For instance, the group property of being cyclic is stronger than the property of being Abelian, because any cyclic group is Abelian.

The opposite of this is weaker than.

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Showing 20 pages using this property.
A
Abelian group +
Nilpotent group  +, Solvable group  +, Metabelian group  +, …
Abelian normal subgroup +
Normal subgroup  +, Solvable normal subgroup  +, Nilpotent normal subgroup  +, …
Abelianness-forcing number +
Nilpotency-forcing number  +, Solvability-forcing number  +
C
Characteristic subgroup +
Normal subgroup  +, Subnormal subgroup  +, Coprime automorphism-invariant subgroup  +, …
Critical subgroup +
Commutator-in-center subgroup  +, Weakly critical subgroup  +, Self-centralizing characteristic subgroup  +, …
Cyclic group +
Abelian group  +, Metacyclic group  +, Polycyclic group  +, …
D
Dedekind group +
Group of nilpotency class two  +, Nilpotent group  +
Derivation-invariant Lie subring +
Ideal of a Lie ring  +
Direct factor of characteristic subgroup +
Subnormal subgroup  +, 2-subnormal subgroup  +, Central factor of characteristic subgroup  +, …
Direct factor of fully invariant subgroup +
Subnormal subgroup  +, 2-subnormal subgroup  +, Direct factor of characteristic subgroup  +, …
F
Finite group +
Finitely generated group  +, Periodic group  +, Group of finite exponent  +, …
Fully invariant subgroup +
Normal subgroup  +, Characteristic subgroup  +, Strictly characteristic subgroup  +, …
G
Group whose automorphism group is cyclic +
Abelian group  +
H
Hall-relatively weakly closed subgroup +
Normal subgroup  +, Coprime automorphism-invariant subgroup  +, Coprime automorphism-invariant normal subgroup  +
I
Inner automorphism +
Class-preserving automorphism  +, Subgroup-conjugating automorphism  +, Normal automorphism  +, …
Isomorph-characteristic subgroup +
Sylow-relatively weakly closed subgroup  +, Isomorph-normal subgroup  +
Isomorph-normal characteristic subgroup +
Normal subgroup  +, Characteristic subgroup  +, Isomorph-normal subgroup  +, …
Isomorph-normal coprime automorphism-invariant subgroup +
Normal subgroup  +, Coprime automorphism-invariant subgroup  +, Coprime automorphism-invariant normal subgroup  +, …
Isomorph-normal subgroup +
Normal subgroup  +
M
Maximal among abelian characteristic subgroups +
Abelian normal subgroup  +, Abelian characteristic subgroup  +
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