On t-pure and almost pure exact sequences of LCA groups

  • 1 Department of Mathematics, Sacred Heart University, 5151 Park Avenue, Fair-field, Connecticut 06825, U.S.A.

Abstract

A proper short exact sequence

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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
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for all positive integers n. We establish conditions under which t-pure exact sequences split and determine those locally compact abelian groups KD (where K is compactly generated and D is discrete) which are t-pure injective or t-pure projective. Calling the extension (*) almost pure if
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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.

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The Journal of Group Theory is devoted to the publication of original research articles in all aspects of group theory. Articles concerning applications of group theory and articles from research areas which have a significant impact on group theory will also be considered.

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