Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Lattice_theorem> ?p ?o. }
Showing items 1 to 22 of
22
with 100 items per page.
- Lattice_theorem abstract "In mathematics, the lattice theorem, sometimes referred to as the fourth isomorphism theorem or the correspondence theorem, states that if is a normal subgroup of a group , then there exists a bijection from the set of all subgroups of such that contains , onto the set of all subgroups of the quotient group . The structure of the subgroups of is exactly the same as the structure of the subgroups of containing with collapsed to the identity element. This establishes a monotone Galois connection between the lattice of subgroups of and the lattice of subgroups of , where the associated closure operator on subgroups of is Specifically, if G is a group, N is a normal subgroup of G, is the set of all subgroups A of G such that , and is the set of all subgroups of G/N, then there is a bijective map such thatfor all One further has that if A and B are in , and A' = A/N and B' = B/N, thenif and only if if then , where is the index of A in B (the number of cosets bA of A in B);where is the subgroup of generated by , and is a normal subgroup of if and only if is a normal subgroup of .This list is far from exhaustive. In fact, most properties of subgroups are preserved in their images under the bijection onto subgroups of a quotient group.Similar results hold for rings, modules, vector spaces, and algebras.".
- Lattice_theorem wikiPageID "1286849".
- Lattice_theorem wikiPageRevisionID "580601230".
- Lattice_theorem hasPhotoCollection Lattice_theorem.
- Lattice_theorem subject Category:Isomorphism_theorems.
- Lattice_theorem type Abstraction100002137.
- Lattice_theorem type Communication100033020.
- Lattice_theorem type IsomorphismTheorems.
- Lattice_theorem type Message106598915.
- Lattice_theorem type Proposition106750804.
- Lattice_theorem type Statement106722453.
- Lattice_theorem type Theorem106752293.
- Lattice_theorem comment "In mathematics, the lattice theorem, sometimes referred to as the fourth isomorphism theorem or the correspondence theorem, states that if is a normal subgroup of a group , then there exists a bijection from the set of all subgroups of such that contains , onto the set of all subgroups of the quotient group . The structure of the subgroups of is exactly the same as the structure of the subgroups of containing with collapsed to the identity element.".
- Lattice_theorem label "Lattice theorem".
- Lattice_theorem label "Théorème de correspondance".
- Lattice_theorem sameAs Théorème_de_correspondance.
- Lattice_theorem sameAs m.04q6mr.
- Lattice_theorem sameAs Q3527189.
- Lattice_theorem sameAs Q3527189.
- Lattice_theorem sameAs Lattice_theorem.
- Lattice_theorem wasDerivedFrom Lattice_theorem?oldid=580601230.
- Lattice_theorem isPrimaryTopicOf Lattice_theorem.