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Higher Structure of Chiral Symmetry. [PDF]
Commun Math PhysCopetti C +3 more
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Transition from neonatal to paediatric intensive care of very preterm-born children: a cohort study of children born between 2013 and 2018 in England and Wales. [PDF]
Arch Dis Child Fetal Neonatal Edvan Hasselt TJ +8 more
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On locally free Abelian groups
Mathematical Notes, 2005An Abelian group is called `locally free' if all its subgroups of finite rank are free. In the present paper it is proved that a torsion-free group is a locally free group if and only if it is a direct limit of an inductive system of finitely generated free groups such that each map in this system is an embedding onto a direct summand (such a system is
exaly +2 more sources
Fully inert subgroups of free Abelian groups
Periodica Mathematica Hungarica, 2014Dikran Dikranjan +2 more
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Torsion-free abelian groups are Borel complete
Annals of Mathematics, 2021We prove that the Borel space of torsion-free Abelian groups with domain $\omega$ 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
G. Paolini, S. Shelah
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On a Free Action of a Group on an Abelian Group
Siberian Mathematical Journal, 2002Let \(G\) be a nontrivial group acting freely on a nonzero Abelian group \(V\), that is, \(vg\neq v\) for all \(1\neq g\in G\), \(0\neq v\in V\), and generated by a set \(X\) of elements of order 3. The authors continue their study of finiteness conditions for \(G\). Considering certain trigonometric equations, they establish the following result: If \(
Mazurov, V. D., Churkin, V. A.
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FREE ABELIAN TOPOLOGICAL GROUPS ON SPHERES
The Quarterly Journal of Mathematics, 1984If X is a completely regular topological space, then the abelian topological group F(X) is a (Markov) free abelian topological group on X if X is a subspace of F(X), X generates F(X) algebraically and for every continuous mapping \(\phi\) of X into any abelian topological group G there exists a continuous homomorphism \(\Phi\) of F(X) into G that ...
Katz, Eli +2 more
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Maximum number of sum-free colorings in finite abelian groups
Israel Journal of Mathematics, 2017An r-coloring of a subset A of a finite abelian group G is called sum-free if it does not induce a monochromatic Schur triple, i.e., a triple of elements a, b, c ∈ A with a + b = c. We investigate κr,G, the maximum number of sum-free r-colorings admitted
Hiêp Hàn, A. Jiménez
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HOMOLOGY OF FREE ABELIANIZED EXTENSIONS OF GROUPS
Mathematics of the USSR-Sbornik, 1992Let \(G\) be a group presented as a factor group \(G = F/N\) of a free group \(F\). Let \(\Phi = F/N'\), which is known as a free abelian extension of \(G\). Ground breaking work on the homology groups of \(\Phi\) with trivial integer coefficients was done by the second author [Commun. Algebra 16, No. 12, 2447-2533 (1988; Zbl 0682.20038)].
Kovács, L. G. +2 more
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On Torsion-Free Abelian k-Groups
Proceedings of the American Mathematical Society, 1987A height sequence s is a function on primes p with values \(s_ p\) natural numbers or \(\infty\). The height sequence \(| x|\) of an element x in a torsion-free abelian group G is defined by \(| x|_ p=height\) of x at p. For a height sequence s, \(G(s)=\{x\in G:| x| \geq s\}\), \(G(ps)=\{x\in G(s):| x|_ p\geq s_ p+1\}\), \(G(s^*)=\{x\in G(s):\sum_{p}(|
Dugas, Manfred, Rangaswamy, K. M.
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