Torsion-free groups, finite rank

Canadian Journal of Mathematics, 1984
This paper deals with two conditions which, when stated, appear similar, but when applied to finitely generated solvable groups have very different effect. We first establish the notation before stating these conditions and their implications. If H is a subgroup of a group G, let denote the setWe say G has the isolator property if is a subgroup for ...
Meier, David, Rhemtulla, Akbar
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Torsion-Free Abelian Groups of Finite Rank with Marked Bases

Journal of Mathematical Sciences, 2021
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FINITE AUTOMORPHISM GROUPS OF TORSION-FREE ABELIAN GROUPS OF FINITE RANK

Mathematics of the USSR-Izvestiya, 1989
A well-known result of Jónsson states that each torsion-free group G of finite rank has a quasi-direct decomposition i.e. a subgroup A of finite index which is a direct sum of pure strongly indecomposable subgroups. For such a group several quasi-direct decompositions do exist all being quasi-isomorphic but generally not isomorphic.
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Self-Cancellation of Torsion-Free Abelian Groups of Finite Rank

Journal of Mathematical Sciences, 2002
An Abelian group \(A\) is said to have self-cancellation if \(A\oplus A\cong A\oplus B\) implies \(A\cong B\). A very simple example of a rank 4 torsion-free Abelian group without the self-cancellation property is constructed. The construction is based on the author's criterion [Algebra Anal. 7, No. 6, 33-78 (1995); corrections ibid. 11, No. 4, 222-224
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abelian groups
torsion-free abelian groups of finite rank
fos: mathematics

algebra and number theory
16. peace & justice
finite rank

nilpotent groups
descriptive set theory
solvable groups, supersolvable groups