Título inglés | Various local global principles for abelian groups. |
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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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