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.
1 | |
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| 1-automorphism-invariant subgroup + | Quasiautomorphism-invariant subgroup +, Strong quasiautomorphism-invariant subgroup +, Characteristic subgroup +, … |
| 1-endomorphism-invariant subgroup + | Quasiendomorphism-invariant subgroup +, Fully invariant subgroup +, 1-automorphism-invariant subgroup +, … |
| 1-isomorphic finite groups + | Order-cum-power statistics-equivalent finite groups +, Power statistics-equivalent finite groups +, Order statistics-equivalent finite groups + |
| 1-isomorphic groups + | Directed power graph-equivalent groups +, Undirected power graph-equivalent groups + |
2 | |
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| 2-hypernormalized subgroup + | Finitarily hypernormalized subgroup +, Intermediately finitarily hypernormalized subgroup +, Hypernormalized subgroup +, … |
| 2-sub-ideal of a Lie ring + | Sub-ideal of a Lie ring + |
| 2-subnormal subgroup + | Conjugate-permutable subgroup +, Join-transitively subnormal subgroup +, Linear-bound join-transitively subnormal subgroup +, … |
3 | |
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| 3-subnormal subgroup + | Subnormal subgroup +, Conjugate-join-closed subnormal subgroup + |
4 | |
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| 4-subnormal subgroup + | Subnormal subgroup + |
A | |
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| AEP-subgroup + | Subgroup in which every subgroup characteristic in the whole group is characteristic + |
| Abelian Lie ring + | Nilpotent Lie ring +, Solvable Lie ring + |
| Abelian characteristic subgroup + | Characteristic subgroup +, Abelian normal subgroup +, Class two characteristic subgroup +, … |
| Abelian conjugacy-closed subgroup + | Conjugacy-closed subgroup + |
| Abelian critical subgroup + | Critical subgroup + |
| Abelian direct factor + | Direct factor +, Central subgroup +, Complemented central factor +, … |
| Abelian group + | Nilpotent group +, Solvable group +, Metabelian group +, … |
| Abelian hereditarily normal subgroup + | Hereditarily normal subgroup +, Transitively normal subgroup + |
| Abelian ideal + | Nilpotent ideal +, Solvable ideal + |
| Abelian normal subgroup + | Normal subgroup +, Commutator-in-center subgroup +, Dedekind normal subgroup +, … |
| Abelian normal subgroup of maximum order + | Abelian normal subgroup of group of prime power order +, Abelian normal subgroup +, Maximal among abelian normal subgroups + |
| Abelian pronormal subgroup + | Pronormal subgroup +, Center of pronormal subgroup +, Central subgroup of pronormal subgroup +, … |
| Abelian subgroup of maximum order + | Maximal among abelian subgroups + |
| Abelian subgroup of maximum order which is normal + | Abelian subgroup of maximum order +, Abelian normal subgroup of group of prime power order +, Abelian normal subgroup +, … |
| Abelian-extensible automorphism-invariant subgroup + | Subgroup of abelian group + |
| Abelian-extensible endomorphism-invariant subgroup + | Subgroup of abelian group + |
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