Property:Weaker than

From Groupprops

The weaker 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 Abelian is weaker than the property of being cyclic, because any cyclic group is Abelian.

The opposite of this is stronger than.

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Showing 20 pages using this property.
A
Abelian group +
Cyclic group  +, Locally cyclic group  +, Finitely generated abelian group  +, …
Abelian normal subgroup +
Central subgroup  +, Cyclic normal subgroup  +, Abelian characteristic subgroup  +, …
Abelianness-forcing number +
Cyclicity-forcing number  +
C
Characteristic subgroup +
Fully invariant subgroup  +, Strictly characteristic subgroup  +, Isomorph-free subgroup  +, …
Coprime automorphism-invariant subgroup +
Characteristic subgroup  +, Coprime automorphism-invariant normal subgroup  +, Hall-relatively weakly closed subgroup  +
Critical subgroup +
Abelian critical subgroup  +, Constructibly critical subgroup  +, C-closed critical subgroup  +
Cyclic group +
Finite cyclic group  +, Group of prime order  +, Odd-order cyclic group  +
D
Derivation-invariant Lie subring +
Lie subring invariant under any derivation with partial divided Leibniz condition powers  +, Self-derivation-invariant Lie subring  +
Direct factor of characteristic subgroup +
Characteristic subgroup  +, Direct factor  +, Minimal normal subgroup  +, …
Direct factor of fully invariant subgroup +
Direct factor  +, Fully invariant subgroup  +
F
Finite group +
Group of prime power order  +, Odd-order group  +
Fully invariant subgroup +
Normal Sylow subgroup  +, Normal Hall subgroup  +, Homomorph-containing subgroup  +, …
G
Group whose automorphism group is cyclic +
Group of prime order  +
H
Hall-relatively weakly closed subgroup +
Isomorph-free subgroup  +, Sylow-relatively weakly closed subgroup  +
I
Inner automorphism +
Inner power automorphism  +
Isomorph-characteristic subgroup +
Isomorph-free subgroup  +
Isomorph-normal characteristic subgroup +
Isomorph-free subgroup  +, Isomorph-characteristic subgroup  +
Isomorph-normal coprime automorphism-invariant subgroup +
Isomorph-normal characteristic subgroup  +
Isomorph-normal subgroup +
Isomorph-free subgroup  +, Isomorph-characteristic subgroup  +, Isomorph-normal characteristic subgroup  +, …
L
Left-transitively WNSCDIN-subgroup +
Characteristic central factor  +
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