Results 121 to 130 of about 252 (156)

Enumerations and Completely Decomposable Torsion-Free Abelian Groups

Theory of Computing Systems, 2009
The main results of this paper are the following: For any family \(R\) of finite sets there exists a completely decomposable torsion-free abelian group \(G_{R}\) of infinite rank such that \(G_{R}\) has an \(X\)-computable copy if and only if \(R\) has a \(\Sigma_{2}^{X}\)-computable enumeration (Theorem 4).
Alexander G Melnikov
exaly   +3 more sources

Direct Decompositions of Torsion-Free Abelian Groups

Lobachevskii Journal of Mathematics, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
exaly   +2 more sources

On Torsion-Free Abelian k-Groups

Proceedings of the American Mathematical Society, 1987
A height sequence s is a function on primes p with values \(s_ p\) natural numbers or \(\infty\). The height sequence \(| x|\) of an element x in a torsion-free abelian group G is defined by \(| x|_ p=height\) of x at p. For a height sequence s, \(G(s)=\{x\in G:| x| \geq s\}\), \(G(ps)=\{x\in G(s):| x|_ p\geq s_ p+1\}\), \(G(s^*)=\{x\in G(s):\sum_{p}(|
Dugas, Manfred, Rangaswamy, K. M.
openaire   +1 more source

On Weakly Transitive Torsion-Free Abelian Groups

Journal of Mathematical Sciences, 2021
This short note adds new information on a previous paper with the same subject by \textit{B. Goldsmith} and \textit{L. Strüngmann} [Commun. Algebra 33, No. 4, 1177--1191 (2005; Zbl 1142.20032)]. The results are: Proposition 2. If \(A\) is a reduced torsion-free group with strongly indecomposable pure subgroups and the set \(T(A)\) of types of all its ...
openaire   +3 more sources

ENDOPRIMAL TORSION-FREE SEPARABLE ABELIAN GROUPS

Journal of Algebra and Its Applications, 2004
We give a characterization for the groups in the title in terms of the graph structure of the critical types occurring in the group. Moreover, we give an example of arbitrarily large endoprimal indecomposable groups.
Göbel, R., Kaarli, K., Márki, L., Wallutis, S. L.   +3 more
openaire   +1 more source

Sums of Complexes in Torsion Free Abelian Groups

Canadian Mathematical Bulletin, 1969
Let A, B, denote two non-void finite complexes (= subsets) of the torsion free abelian group G,Let d(A),… denote the maximum number of linearly independent elements of A,… and let n = n(A, B) denote the number of elements of A + B whose representation in the form a + b is unique. In the preceding paper, Tarwater and Entringer [1] proved that n ≥ d(A).
Heilbronn, H., Scherk, P.
openaire   +4 more sources

Local Abelian Torsion-Free Groups

Journal of Mathematical Sciences, 2014
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +1 more source

Enumerations and Torsion Free Abelian Groups

2007
We study possible spectrums of torsion free Abelian groups. We code families of finite sets into group and set up the correspondence between their algorithmic complexities.
openaire   +1 more source

A NOTE ON HOMOGENEOUS TORSION-FREE ABELIAN GROUPS

The Quarterly Journal of Mathematics, 1984
Let \(\tau\) be a type of a rational group and let \(\kappa\) be an infinite cardinal. A (torsion-free abelian) group G is called \(\kappa\)-homogeneous of type \(\tau\) if every pure subgroup of G of rank less than \(\kappa\) is a homogeneous completely decomposable group of type \(\tau\).
openaire   +2 more sources

Tight subgroups in torsion-free Abelian groups

Israel Journal of Mathematics, 2003
The paper deals with ``tight subgroups'' of torsion-free Abelian groups, namely those subgroups that are maximal with respect to being completely decomposable. Tight subgroups were first studied by \textit{K. Benabdallah}, \textit{A. Mader} and \textit{M. A. Ould-Beddi} [J. Algebra 225, No.
Ould-Beddi, Mohamed A., Strüngmann, Lutz   +1 more
openaire   +2 more sources