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Torsion-free Abelian Groups Revisited [PDF]
Rendiconti del Seminario Matematico della Università di Padova, 2019 Let G be a torsion-free abelian group of finite rank. The orbits of the action of Aut( G ) on the set of maximal independent subsets of
Phill Schultz
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On the Indecomposability of Torsion-Free Abelian Groups [PDF]
Proceedings of the American Mathematical Society, 1965 1. We consider the following question posed by E. Weinberg [4, ?5.2]: Does there exist a torsion-free abelian group of cardinality greater than the continuum (K) with the property that each pure subgroup is (directly) indecomposable? In ?2 we answer this question negatively for a large class of groups which contains, most notably, the class of ...
Josh Armstrong
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A Note on the Square Subgroups of Decomposable Torsion-Free Abelian Groups of Rank Three [PDF]
Annales Mathematicae Silesianae, 2018 A hypothesis stated in [16] is confirmed for the case of associative rings. The answers to some questions posed in the mentioned paper are also given. The square subgroup of a completely decomposable torsion-free abelian group is described (in both cases
Woronowicz Mateusz
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Torsion-Free Abelian Groups are Borel Complete [PDF]
Annals of Mathematics, 2021 We prove that the Borel space of torsion-free Abelian groups with domain $ω$ is Borel complete, i.e., the isomorphism relation on this Borel space is as complicated as possible, as an isomorphism relation. This solves a long-standing open problem in descriptive set theory, which dates back to the seminal paper on Borel reducibility of Friedman and ...
Gianluca Paolini, Saharon Shelah
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Sums of Complexes in Torsion Free Abelian Groups [PDF]
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).
H. Heilbronn, Peter Scherk
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Decompositions of torsion-free abelian groups [PDF]
Journal of Algebra, 2018 All groups in this review are abelian and torsion-free. Some concepts like near-isomorphism, sufficient-isomorphism, mono-equivalence, main decomposition, the length of a decomposition, strongly-separable groups, quasi-separable groups, \(\tau\)-homogeneous groups, \(\tau\)-clipped groups for any type \(\tau\) and various kinds of types have been ...
Gabor Braun. Phill Schultz +1 more
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Protori and Torsion-Free Abelian Groups [PDF]
, 2019 The Resolution Theorem for Compact Abelian Groups is applied to show that the profinite subgroups of a finite-dimensional compact connected abelian group (protorus) which induce tori quotients comprise a lattice under intersection (meet) and $+$ (join), facilitating a proof of the existence of a universal resolution.
Wayne Lewis
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On quasi-decomposition of torsion free Abelian groups [PDF]
Proceedings of the American Mathematical Society, 1962 James D. Reid
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Torsion-free Extensions of Torsion-free Abelian Groups of Finite Rank
, 2009 Duisburg, Essen, Univ., Diss ...
Stefan Friedenberg
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Solving logistic tasks by parallelizing algorithms of the theory of direct decompositions of torsion-free abelian groups [PDF]
E3S Web of Conferences, 2023 The paper considers the principles of parallelization at marshalling yards and determines their importance. There are presented the methods for direct decompositions of torsion-free Abelian groups of finite rank.
Blagoveshchenskaya E. +2 more
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