A Topology for Primary Abelian Groups

Doyle O. Cutler and Robert W. Stringall
Additional contact information
Doyle O. Cutler: 24 University of California
Robert W. Stringall: 24 University of California

Chapter [5] in Études sur les Groupes abéliens / Studies on Abelian Groups, 1968, pp 93-100 from Springer

Abstract: Abstract Let B be a p-primary abelian group without elements of infinite height, let B be a basic subgroup of G and B̅ the torsion subgroup of the completion of B with respect to the p-adic topology. If no is the collection of all fully invariant subgroups of G with the additional property that L ∈ no implies B+L = G, for all basic subgroups B of G, then n induces a Hausdorff topology on G whose completion Ĝ is isomorphic to B̅ (†) If H is a pure subgroup of G and if B is a basic subgroup of H, then the topology constructed for H and the relative topology agree. Homomorphisms between p-groups without elements of infinite height are continuous. Moreover, if H1 is a dense subgroup of G. and if G has no elements of infinite height, then any homomorphism of H1 onto G can be extended uniquely to a homomorphism of G onto Ĝ.

Keywords: Abelian Group; Finite Order; Relative Topology; Infinite Order; Large Subgroup (search for similar items in EconPapers)
Date: 1968
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-46146-0_5

Ordering information: This item can be ordered from
http://www.springer.com/9783642461460

DOI: 10.1007/978-3-642-46146-0_5

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().