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On Sum-Free Subsets of Abelian Groups
Axioms, 2023 In this paper, we discuss some of the key properties of sum-free subsets of abelian groups. Our discussion has been designed with a broader readership in mind and is hence not overly technical.
Renato Cordeiro de Amorim
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Hodge-Deligne polynomials of character varieties of free abelian groups [PDF]
Open Mathematics, 2021 Let FF be a finite group and XX be a complex quasi-projective FF-variety. For r∈Nr\in {\mathbb{N}}, we consider the mixed Hodge-Deligne polynomials of quotients Xr/F{X}^{r}\hspace{-0.15em}\text{/}\hspace{-0.08em}F, where FF acts diagonally, and compute ...
Florentino Carlos, Silva Jaime
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On Superstable Expansions of Free Abelian Groups [PDF]
Notre Dame Journal of Formal Logic, 2014 We prove that (Z;+;0) has no proper superstable expansions of finite Lascar rank.Nevertheless,weexhibitasuperstableproperexpansion. 1 Introduction Thispaperfitsintothegeneralframeworkofaddinganewpredicatetoawellbehavedstructureand asking whether the ...
D. Palacín, R. Sklinos
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A characterization of free abelian groups [PDF]
Proceedings of the American Mathematical Society, 1985 In the category of abelian groups, being free is equivalent to having a discrete norm.
J. Steprāns
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Small points and free abelian groups [PDF]
International Mathematics Research Notices, 2014 Let $F$ be an algebraic extension of the rational numbers and $E$ an elliptic curve defined over some number field contained in $F$. The absolute logarithmic Weil height, respectively the N\'eron-Tate height, induces a norm on $F^*$ modulo torsion ...
R. Grizzard +2 more
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From free abelian groups to free abelian ℓ-groups
Mathematica Slovaca, 2011 Abstract For each n, the free abelian group F on countably many free generators will be equipped with a monoid P n making (F,P n) into the free n-generator abelian ℓ-group. This is a generalization of the main result of the second author, published in the J. Pure Appl.
Daniele Mundici
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More Abelian groups with free duals [PDF]
Portugaliae Mathematica, 2011 In answer to a question of A. Blass, J. Irwin and G. Schlitt, a subgroup G of the additive group Z^{\omega} is constructed whose dual, Hom(G,Z), is free abelian of rank 2^{\aleph_0}.
Bergman, George M.
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The isomorphism problem for torsion-free Abelian groups is analytic complete
Journal of Algebra, 2008 We prove that the isomorphism problem for torsion-free Abelian groups is as complicated as any isomorphism problem could be in terms of the analytical hierarchy, namely 1 complete.
Rod Downey, Antonio Montalban
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Diophantine problems in solvable groups [PDF]
Bulletin of Mathematical Sciences, 2020 We study the Diophantine problem (decidability of finite systems of equations) in different classes of finitely generated solvable groups (nilpotent, polycyclic, metabelian, free solvable, etc.), which satisfy some natural “non-commutativity” conditions.
Albert Garreta +2 more
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Non-∀-homogeneity in free groups
Bulletin of Mathematical Sciences, 2021 We prove that non-abelian free groups of finite rank at least 3 or of countable rank are not ∀-homogeneous. We answer three open questions from Kharlampovich, Myasnikov, and Sklinos regarding whether free groups, finitely generated elementary free groups,
Olga Kharlampovich, Christopher Natoli
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