Results 171 to 180 of about 2,524 (214)

Near Isomorphism for a Class of Infinite Rank Torsion-Free Abelian Groups

Communications in Algebra, 2007
The notion of “near isomorphism” for torsion-free Abelian groups of finite rank is well known. In particular, this concept turned out to be of importance for classifying almost completely decomposable groups. We extend near isomorphism to classes of torsion-free Abelian groups of infinite rank which are unions of bcd–groups, this is to say unions of ...
Ekaterina Blagoveshchenskaya, Lutz Strüngmann   +1 more
openaire   +2 more sources

Direct decomposition theory under near-isomorphism for a class of infinite rank torsion-free abelian groups

Journal of Group Theory, 2016
Abstract Near-isomorphism is known as the right concept for classification theorems in the theory of almost completely decomposable groups. As a natural generalization the authors extended in [6] the notion of near-isomorphism to Abelian groups of arbitrary rank.
Blagoveshchenskaya, Ekaterina, Strüngmann, Lutz H.   +1 more
openaire   +2 more sources

Torsion-Free Groups of Infinite Rank

2015
This chapter continues the theme of torsion-free groups, this time for the infinite rank case. There is no shortage of relevant results.
L. Fuchs
openaire   +2 more sources

On the Structure of Torsion-free Groups of Infinite Rank

Abelian Groups, 2022
P. Hill
openaire   +2 more sources

On the Residual Finiteness of a Class of Infinite Soluble Groups

Algebra Colloquium, 2022
Let [Formula: see text] be a completely decomposable homogeneous torsion-free abelian group of rank [Formula: see text] ([Formula: see text]). Let [Formula: see text] be the split extension of [Formula: see text] by an automorphism [Formula: see text ...
J. Liao, H. Liu, Xiaoliang Luo, Xingzhong Xu   +3 more
semanticscholar   +1 more source

Abelian Groups

, 2022
Friedrich Wilhelm Levi, 1888-1966, L. Fuchs and R. Gobel. Part 1 Survey articles: finite rank butler groups - a survey of recent results, D. Arnold and C. Vinsonhaler set-theoretic methods - the use of gamma invariants, P.C.
L. Fuchs, R. Göbel
semanticscholar   +1 more source

THE GENERATING GRAPH OF INFINITE ABELIAN GROUPS

Bulletin of the Australian Mathematical Society, 2019
For a group $G$ , let $\unicode[STIX]{x1D6E4}(G)$ denote the graph defined on the elements of $G$ in such a way that two distinct vertices are connected by an edge if and only if they generate $G$ . Let $\unicode[STIX]{x1D6E4}^{\ast }(G)$ be the subgraph
C. Acciarri, A. Lucchini
semanticscholar   +1 more source

A Generalization of Quotient Divisible Groups to the Infinite Rank Case

Siberian mathematical journal, 2021
A. Tsarev
semanticscholar   +2 more sources

Mordell–Weil groups over large algebraic extensions of fields of characteristic zero

Research in Number Theory
We study the structure of the Mordell–Weil groups of semiabelian varieties over large algebraic extensions of a finitely generated field of characteristic zero. We consider two types of algebraic extensions in this paper; one is of extensions obtained by
Takuya Asayama, Yuichiro Taguchi
semanticscholar   +1 more source

Direct Decompositions of Torsion-Free Abelian Groups

Lobachevskii Journal of Mathematics, 2020
E. Blagoveshchenskaya
semanticscholar   +1 more source