Various local global principles for abelian groups.

Título inglés Various local global principles for abelian groups.
Título español Diversos principios globales locales para grupos abelianos.
Autor/es Peschke, George ; Symonds, Peter
Organización Dep. Math. Sci. Univ. Alberta, Edmonton (Alberta), Canadá;Dep. Math. Northwestern Univ., Evanston (Illinois), Estados Unidos
Revista 0214-1493
Publicación 1994, 38 (2): 353-370, 10 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés We discuss local global principles for abelian groups by examining the adjoint functor pair obtained by (left adjoint) sending an abelian group A to the local diagram L(A) = {Z(p) Ä A → Q Ä A} and (right adjoint) applying the inverse limit functor to such diagrams; p runs through all integer primes. We show that the natural map A → lim L(A) is an isomorphism if A has torsion at only finitely many primes. If A is fixed we answer the genus problem of identifying all those groups B for which the local diagrams L(A) and L(B) are isomorphic. A similar analysis is carried out for the arithmetic systems S(A) = {QÄA → QÄA^ ← A^} and the local systems {QÄA → QÄ(ΠZ(p)ÄA) ←
Π(Z(p)ÄA)}. The delicate relationship between the various adjoint functor pairs described above is explained.
Clasificación UNESCO 120106
Palabras clave español Grupos abelianos ; Grupo nilpotente
Código MathReviews MR1316632
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