EuDML | Browse

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

Displaying 1 – 11 of 11

Currently displaying 1 – 11 of 11