Displaying similar documents to “A note on the countable extensions of separable p ω + n -projective abelian p -groups”

On countable extensions of primary abelian groups

Peter Vassilev Danchev (2007)

Archivum Mathematicum

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It is proved that if A is an abelian p -group with a pure subgroup G so that A / G is at most countable and G is either p ω + n -totally projective or p ω + n -summable, then A is either p ω + n -totally projective or p ω + n -summable as well. Moreover, if in addition G is nice in A , then G being either strongly p ω + n -totally projective or strongly p ω + n -summable implies that so is A . This generalizes a classical result of Wallace (J. Algebra, 1971) for totally projective p -groups as well as continues our recent investigations...

Notes on countable extensions of  p ω + n -projectives

Peter Vassilev Danchev (2008)

Archivum Mathematicum

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We prove that if G is an Abelian p -group of length not exceeding ω and H is its p ω + n -projective subgroup for n ∈ ℕ ∪ { 0 } such that G / H is countable, then G is also p ω + n -projective. This enlarges results of ours in (Arch. Math. (Brno), 2005, 2006 and 2007) as well as a classical result due to Wallace (J. Algebra, 1971).

On extensions of primary almost totally projective abelian groups

Peter Vassilev Danchev (2008)

Mathematica Bohemica

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Suppose G is a subgroup of the reduced abelian p -group A . The following two dual results are proved: ( * ) If A / G is countable and G is an almost totally projective group, then A is an almost totally projective group. ( * * ) If G is countable and nice in A such that A / G is an almost totally projective group, then A is an almost totally projective group. These results somewhat strengthen theorems due to Wallace (J. Algebra, 1971) and Hill (Comment. Math. Univ. Carol., 1995), respectively. ...