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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Pages using the property "Stronger than"
Showing 25 pages using this property.
2 | |
|---|
| 2-hypernormalized subgroup + | Finitarily hypernormalized subgroup +, 2-subnormal subgroup +, Hypernormalized subgroup +, … |
| 2-subnormal subgroup + | Conjugate-permutable subgroup +, Subnormal subgroup +, Join of finitely many 2-subnormal subgroups +, … |
3 | |
|---|
| 3-subnormal subgroup + | Subnormal subgroup +, Conjugate-join-closed subnormal subgroup + |
A | |
|---|
| Abelian Lie ring + | Nilpotent Lie ring +, Solvable Lie ring + |
| Abelian characteristic subgroup + | Abelian normal subgroup +, Class two characteristic subgroup +, Nilpotent characteristic subgroup + |
| Abelian conjugacy-closed subgroup + | Conjugacy-closed subgroup + |
| Abelian normal subgroup + | Commutator-in-center subgroup +, Class two normal subgroup +, Nilpotent normal subgroup +, … |
| Abelian subgroup of maximum order + | Maximal among Abelian subgroups + |
| Abelianness-forcing number + | Nilpotence-forcing number +, Solvability-forcing number + |
| Abnormal subgroup + | Self-normalizing subgroup +, Weakly abnormal subgroup +, Subabnormal subgroup +, … |
| Additive group of a field + | Characteristically simple group +, Abelian group +, Elementary Abelian group + |
| Alternative loop + | Power-associative loop +, Algebra loop +, Quasigroup + |
| Amalgam-characteristic subgroup + | Potentially characteristic subgroup +, Normal subgroup + |
| Ambivalent group + | Group in which every square is a commutator +, Square-in-derived group + |
| Auto-invariance property + | Endo-invariance property +, Invariance property +, Strongly join-closed subgroup property +, … |
| Automorph-conjugate subgroup + | Intersection of automorph-conjugate subgroups +, Join of automorph-conjugate subgroups +, Core-characteristic subgroup +, … |
| Automorph-join-closed subnormal subgroup + | Conjugate-join-closed subnormal subgroup +, Finite-automorph-join-closed subnormal subgroup +, Finite-conjugate-join-closed subnormal subgroup + |
| Automorphism-based relation-implication-expressible subgroup property + | Centralizer-closed subgroup property +, Normalizer-closed subgroup property + |
| Automorphism-faithful AEP-subgroup + | Sectionally AEP-subgroup +, AEP-subgroup + |
| Automorphism-faithful subgroup + | Coprime automorphism-faithful subgroup + |
B | |
|---|
| Base of a wreath product + | Subset-conjugacy-closed subgroup +, Conjugacy-closed subgroup +, 2-subnormal subgroup +, … |
| Binate group + | Acyclic group + |
| Bound-word subgroup + | Strictly characteristic subgroup + |
| Bounded Engel group + | Engel group +, Nilpotent group + |
C | |
|---|
| C-closed critical subgroup + | Critical subgroup +, C-closed self-centralizing subgroup +, C-closed subgroup + |
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