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On t-pure and almost pure exact sequences of LCA groups
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Peter Loth
Published/Copyright:
February 12, 2007
Abstract
A proper short exact sequence
in the category of locally compact abelian groups is said to be t-pure if φ(A) is a topologically pure subgroup of B, that is, if
for all positive integers n. We establish conditions under which t-pure exact sequences split and determine those locally compact abelian groups K ⊕ D (where K is compactly generated and D is discrete) which are t-pure injective or t-pure projective. Calling the extension (*) almost pure if
for all positive integers n, we obtain a complete description of the almost pure injectives and almost pure projectives in the category of locally compact abelian groups.
Received: 2005-08-28
Revised: 2005-12-06
Published Online: 2007-02-12
Published in Print: 2006-11-28
© Walter de Gruyter
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Articles in the same Issue
- Crossover Morita equivalences for blocks of the covering groups of the symmetric and alternating groups
- On a theorem of Artin. II
- Cycle index methods for finite groups of orthogonal type in odd characteristic
- Characterization of injectors in finite soluble groups
- Some class size conditions implying solvability of finite groups
- On t-pure and almost pure exact sequences of LCA groups
- Translation equivalent elements in free groups
- On representing words in the automorphism group of the random graph
