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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Pages using the property "Weaker than"
Showing 25 pages using this property.
1 | |
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| 1-automorphism-invariant subgroup + | 1-endomorphism-invariant subgroup + |
| 1-isomorphic groups + | Isomorphic groups + |
2 | |
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| 2-cocycle for a group action + | 2-coboundary for a group action +, Symmetric 2-cocycle for a group action +, Normalized 2-cocycle for a group action + |
| 2-cocycle for trivial group action + | 2-coboundary for trivial group action +, Symmetric 2-cocycle for trivial group action +, Skew-symmetric 2-cocycle for trivial group action +, … |
| 2-hypernormalized subgroup + | Normal subgroup + |
| 2-sub-ideal of a Lie ring + | Ideal of a Lie ring + |
| 2-subnormal subgroup + | Base of a wreath product +, Normal subgroup +, 2-hypernormalized subgroup +, … |
3 | |
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| 3-subnormal subgroup + | Normal subgroup +, 2-subnormal subgroup +, Commutator of a 2-subnormal subgroup and a subset + |
4 | |
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| 4-subnormal subgroup + | Normal subgroup +, 2-subnormal subgroup +, 3-subnormal subgroup + |
A | |
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| ACU-closed group property + | Varietal group property +, Union-closed group property +, Directed union-closed group property +, … |
| ACU-closed subgroup property + | Join-closed subgroup property +, Union-closed subgroup property +, Directed union-closed subgroup property + |
| AEP-subgroup + | Direct factor +, Base of a wreath product +, Fully normalized subgroup +, … |
| Abelian Lie ring + | Cyclic Lie ring + |
| Abelian characteristic subgroup + | Cyclic characteristic subgroup +, Characteristic central subgroup +, Abelian critical subgroup +, … |
| Abelian group + | Cyclic group +, Homocyclic group +, Finite abelian group +, … |
| Abelian group of prime power order + | Cyclic group of prime power order +, Homocyclic group of prime power order +, Finite elementary abelian group + |
| Abelian hereditarily normal subgroup + | Central subgroup +, Cyclic normal subgroup + |
| Abelian ideal + | Central ideal + |
| Abelian normal subgroup + | Abelian direct factor +, Central subgroup +, Cyclic normal subgroup +, … |
| Abelian normal subgroup of maximum order + | Abelian subgroup of maximum order which is normal + |
| Abelian normal subgroup of maximum rank + | Elementary Abelian normal subgroup of maximum rank + |
| Abelian pronormal subgroup + | Central subgroup +, Abelian normal subgroup +, Abelian Sylow subgroup + |
| Abelian subgroup + | Central subgroup +, Abelian normal subgroup +, Abelian characteristic subgroup +, … |
| Abelian subgroup of maximum rank + | Maximal among abelian subgroups of maximum rank +, Elementary abelian subgroup of maximum rank + |
| Abelian-extensible automorphism-invariant subgroup + | Characteristic subgroup of abelian group +, Abelian-potentially characteristic subgroup +, Subgroup of finite abelian group + |
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