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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 $n \in ℕ \cup {0}$ 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).

Notes on mixed groups II

Phillip Schultz (1986)

Rendiconti del Seminario Matematico della Università di Padova

Number of indecomposable summands in direct decompositions of torsion-free abelian groups

L. Fuchs, P. Gräbe (1975)

Rendiconti del Seminario Matematico della Università di Padova

Number of solutions in a box of a linear equation in an Abelian group

Maciej Zakarczemny (2016)

Colloquium Mathematicae

For every finite Abelian group Γ and for all $g, a ₁, . . ., a_{k} \in Γ$ , if there exists a solution of the equation $\sum_{i = 1}^{k} a_{i} x_{i} = g$ in non-negative integers $x_{i} \leq b_{i}$ , where $b_{i}$ are positive integers, then the number of such solutions is estimated from below in the best possible way.

Number of solutions in a box of a linear homogeneous equation in an Abelian group

Maciej Zakarczemny (2012)

Acta Arithmetica

On a class of abelian p-groups.

Manfred Dugas, John Irwin (1992)

Forum mathematicum

On a class of Butler groups.

Laszlo Fuchs, Claudia Metelli (1991)

Manuscripta mathematica

On a class of locally Butler groups

Ladislav Bican (1991)

Commentationes Mathematicae Universitatis Carolinae

A torsionfree abelian group $B$ is called a Butler group if $B e x t (B, T) = 0$ for any torsion group $T$ . It has been shown in [DHR] that under $C H$ any countable pure subgroup of a Butler group of cardinality not exceeding $ℵ_{ω}$ is again Butler. The purpose of this note is to show that this property has any Butler group which can be expressed as a smooth union $\cup_{α < μ} B_{α}$ of pure subgroups $B_{α}$ having countable typesets.

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Most abelian p-groups are determined by the Jacobson radical of their endomorphism rings.

Multiple Tilings of n-Dimensional Space by Unit Cubes.

Mutations in finite groups.

$N$ -pure-high subgroups of abelian groups

Nice bases for mixed and torsion-free Abelian groups.

Non-integer lattice tilings by (k, n) truncated crosses.

Note on Direct Decompositions of Torsion-free Abelian Groups

Note on initial topologies on rational vector spaces induced by revalued linear mappings.

Note on quasi-isomorphism of torsion free abelian groups of finite rank (Preliminary communication)

Notes on countable extensions of $p^{ω + n}$ -projectives