Correspondence theorem

Correspondence theorem   (Redirected from Lattice theorem) Jump to navigation Jump to search In group theory, the correspondence theorem[1][2][3][4][5][6][7][8] (also the lattice theorem,[9] and variously and ambiguously the third and fourth isomorphism theorem[6][10]) states that if {displaystyle N} is a normal subgroup of a group {displaystyle G} , then there exists a bijection from the set of all subgroups {displaystyle A} of {displaystyle G} containing {displaystyle N} , onto the set of all subgroups of the quotient group {displaystyle G/N} . The structure of the subgroups of {displaystyle G/N} is exactly the same as the structure of the subgroups of {displaystyle G} containing {displaystyle N} , with {displaystyle N} collapsed to the identity element.

Specifically, if G is a group, {displaystyle Ntriangleleft G} , a normal subgroup of G, {displaystyle {mathcal {G}}={Amid Nsubseteq A

Si quieres conocer otros artículos parecidos a Correspondence theorem puedes visitar la categoría Isomorphism theorems.

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