# Various local global principles for abelian groups.

Publicacions Matemàtiques (1994)

- Volume: 38, Issue: 2, page 353-370
- ISSN: 0214-1493

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topPeschke, George, and Symonds, Peter. "Various local global principles for abelian groups.." Publicacions Matemàtiques 38.2 (1994): 353-370. <http://eudml.org/doc/41185>.

@article{Peschke1994,

abstract = {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) ⊗ A → Q ⊗ 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) = \{Q⊗A → Q⊗A^ ← A^\} and the local systems \{Q⊗A → Q⊗(ΠZ(p)⊗A) ← Π(Z(p)⊗A)\}. The delicate relationship between the various adjoint functor pairs described above is explained.},

author = {Peschke, George, Symonds, Peter},

journal = {Publicacions Matemàtiques},

keywords = {Grupos abelianos; Grupo nilpotente; adjoint functor pairs; localizations for Abelian groups; genus problem; local diagrams},

language = {eng},

number = {2},

pages = {353-370},

title = {Various local global principles for abelian groups.},

url = {http://eudml.org/doc/41185},

volume = {38},

year = {1994},

}

TY - JOUR

AU - Peschke, George

AU - Symonds, Peter

TI - Various local global principles for abelian groups.

JO - Publicacions Matemàtiques

PY - 1994

VL - 38

IS - 2

SP - 353

EP - 370

AB - 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) ⊗ A → Q ⊗ 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) = {Q⊗A → Q⊗A^ ← A^} and the local systems {Q⊗A → Q⊗(ΠZ(p)⊗A) ← Π(Z(p)⊗A)}. The delicate relationship between the various adjoint functor pairs described above is explained.

LA - eng

KW - Grupos abelianos; Grupo nilpotente; adjoint functor pairs; localizations for Abelian groups; genus problem; local diagrams

UR - http://eudml.org/doc/41185

ER -

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