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Tight subgroups in torsion-free Abelian groups
Israel Journal of Mathematics, 2003The 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. +1 more
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A NOTE ON HOMOGENEOUS TORSION-FREE ABELIAN GROUPS
The Quarterly Journal of Mathematics, 1984Let \(\tau\) 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 \(\tau\).
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2000
There are two equivalence relations on torsion-free abelian groups that are weaker than group isomorphism, namely quasi-isomorphism and isomorphism at a prime p. Properties of these equivalence relations are conveniently expressed in a categorical setting.
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There are two equivalence relations on torsion-free abelian groups that are weaker than group isomorphism, namely quasi-isomorphism and isomorphism at a prime p. Properties of these equivalence relations are conveniently expressed in a categorical setting.
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Superposition for divisible torsion-free abelian groups
1998Variable overlaps are one of the main sources for the inefficiency of AC or ACU theorem proving calculi. In the presence of the axioms of abelian groups or at least cancellative abelian monoids, ordering restrictions allow us to avoid some of these overlaps, but inferences with unshielded variables remain necessary.
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On Torsion-Free Minimal Abelian Groups
Communications in Algebra, 2005ABSTRACT An abelian group is said to be minimal if it is isomorphic to all its subgroups of finite index. In this article we show that torsion-free groups which are complete in their ℤ-adic topology or are of p-rank not greater than 1, for all primes p, are minimal.
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On a Class of Torsion-Free Abelian Groups
Proceedings of the London Mathematical Society, 1970openaire +2 more sources
On direct decompositions of torsion free abelian groups
Publicationes Mathematicae Debrecen, 2022openaire +1 more source
The abelian groups with torsion-free endomorphism ring
Publicationes Mathematicae Debrecen, 2022openaire +2 more sources
Countable Torsion-Free Abelian Groups
Proceedings of the London Mathematical Society, 1960openaire +2 more sources