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Torsion-free abelian groups revisited [PDF]

Rendiconti del Seminario Matematico della Università di Padova, 2020
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
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On Undecidability of Finite Subsets Theory for Torsion Abelian Groups

Mathematics, 2022
Let M be a commutative cancellative monoid with an element of infinite order. The binary operation can be extended to all finite subsets of M by the pointwise definition. So, we can consider the theory of finite subsets of M.
Sergey Mikhailovich Dudakov
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Regularity in torsion-free abelian groups [PDF]

Czechoslovak Mathematical Journal, 1992
Eine Untergruppe \(B\) einer torsionsfreien abelschen Gruppe \(A\) heißt regulär (kritisch regulär) falls \(t^ B(b) = t^ A(b)\) für alle \(b\in B\) (falls für alle Typen \(t\) gilt: \(B(t) \setminus B^*(t)_ * \subset A(t)\setminus A^*(t)_ *\)). Die Untergruppe \(B\) heißt stark regulär, falls \(B\) eine reguläre und eine kritisch reguläre Untergruppe ...
Müller, Edgar, Mutzbauer, Otto
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On Some Results of a Torsion-Free Abelian Kernel Group

Recoletos Multidisciplinary Research Journal, 2014
In [6], for any torsion-free abelian groups Gand H, the kernel of Hin GisfHGGHHomfker, ker,. The kernel of Hin Gis a pure fully invariant subgroup of G.
Ricky B. Villeta
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On Some Results of a Torsion-Free Abelian Trace Group

Recoletos Multidisciplinary Research Journal, 2014
In [6], givenany torsion-free abelian groups Gand H, the pure trace of Hin Gis *,:,GHHomfHfGHtr which is equivalent to the set ZnGHHomfHfngGgsomefor ,,:.The pure trace GHtr, is a pure fully invariant subgroup of G.
Ricky B. Villeta
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A Distinguished Subgroup of Compact Abelian Groups

Axioms, 2022
Here “group” means additive abelian group. A compact group G contains δ–subgroups, that is, compact totally disconnected subgroups Δ such that G/Δ is a torus.
Dikran Dikranjan, Wayne Lewis, Peter Loth, Adolf Mader   +3 more
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A Note on Additive Groups of Some Specific Torsion-Free Rings of Rank Three and Mixed Associative Rings

Discussiones Mathematicae - General Algebra and Applications, 2017
It is studied how rank two pure subgroups of a torsion-free Abelian group of rank three influences its structure and type set. In particular, the criterion for such a subgroup B to be a direct summand of a torsion-free Abelian group of rank three with ...
Najafizadeh Alireza, Woronowicz Mateusz
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Type II string theory on Calabi-Yau manifolds with torsion and non-Abelian discrete gauge symmetries

Journal of High Energy Physics, 2017
We provide the first explicit example of Type IIB string theory compactification on a globally defined Calabi-Yau threefold with torsion which results in a four-dimensional effective theory with a non-Abelian discrete gauge symmetry. Our example is based
Volker Braun, Mirjam Cvetič, Ron Donagi, Maximilian Poretschkin   +3 more
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Indecomposable decompositions of torsion-free abelian groups [PDF]

Journal of Algebra, 2018
An indecomposable decomposition of a torsion-free abelian group $G$ of rank $n$ is a decomposition $G=A_1\oplus\cdots\oplus A_t$ where $A_i$ is indecomposable of rank $r_i$ so that $\sum_i r_i=n$ is a partition of $n$. The group $G$ may have decompositions that result in different partitions of $n$.
Adolf Mader, Phill Schultz
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Characterization of the automorphisms having the lifting property in the category of abelian p-groups

International Journal of Mathematics and Mathematical Sciences, 2003
Let p be a prime. It is shown that an automorphism α of an abelian p-group A lifts to any abelian p-group of which A is a homomorphic image if and only if α=π idA, with π an invertible p-adic integer.
S. Abdelalim, H. Essannouni
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