Displaying similar documents to “On elongations of totally projective p -groups by p ω + n -projective 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...

A note on the countable extensions of separable p ω + n -projective abelian p -groups

Peter Vassilev Danchev (2006)

Archivum Mathematicum

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It is proved that if G is a pure p ω + n -projective subgroup of the separable abelian p -group A for n ∈ N ∪ { 0 } such that | A / G | ≤ ℵ 0 , then A is p ω + n -projective as well. This generalizes results due to Irwin-Snabb-Cutler (CommentṀathU̇nivṠtṖauli, 1986) and the author (Arch. Math. (Brno), 2005).

Countable extensions of torsion Abelian groups

Peter Vassilev Danchev (2005)

Archivum Mathematicum

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Suppose A is an abelian torsion group with a subgroup G such that A / G is countable that is, in other words, A is a torsion countable abelian extension of G . A problem of some group-theoretic interest is that of whether G ∈ 𝕂 , a class of abelian groups, does imply that A ∈ 𝕂 . The aim of the present paper is to settle the question for certain kinds of groups, thus extending a classical result due to Wallace (J. Algebra, 1981) proved when 𝕂 coincides with the class of all totally projective p -groups. ...