Displaying similar documents to “Small-sum pairs in abelian groups”

Representation of finite abelian group elements by subsequence sums

David J. Grynkiewicz, Luz E. Marchan, Oscar Ordaz (2009)

Journal de Théorie des Nombres de Bordeaux

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Let G ≅ C n 1 ⊕ ... ⊕ C n r be a finite and nontrivial abelian group with n 1 | n 2 | ... | n r . A conjecture of Hamidoune says that if W = w 1 · ... · w n is a sequence of integers, all but at most one relatively prime to | G | , and S is a sequence over G with | S | ≥ | W | + | G | - 1 ≥ | G | + 1 , the maximum multiplicity of S at most | W | , and σ ( W ) ≡ 0 mod | G | , then there exists a nontrivial subgroup H such that every element g ∈ H can be represented as a weighted subsequence sum of the form g = ∑ n i = 1 w i s i , with s 1 · ... · s n a subsequence of S . We give two examples showing this does not hold in general, and characterize the...

Characterizations of groups generated by Kronecker sets

András Biró (2007)

Journal de Théorie des Nombres de Bordeaux

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In recent years, starting with the paper [B-D-S], we have investigated the possibility of characterizing countable subgroups of the torus T = R / Z by subsets of Z . Here we consider new types of subgroups: let K ⊆ T be a Kronecker set (a compact set on which every continuous function f : K → T can be uniformly approximated by characters of T ), and G the group generated by K . We prove (Theorem 1) that G can be characterized by a subset of Z 2 (instead of a subset of Z ). If K is finite, Theorem 1 implies our...

On the vanishing of Iwasawa invariants of absolutely abelian p-extensions

Gen Yamamoto (2000)

Acta Arithmetica

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1. Introduction. Let p be a prime number and ℤ p the ring of p-adic integers. Let k be a finite extension of the rational number field ℚ, k ∞ a ℤ p -extension of k, k n the nth layer of k ∞ / k , and A n the p-Sylow subgroup of the ideal class group of k n . Iwasawa proved the following well-known theorem about the order A n of A n : Theorem A (Iwasawa). Let k ∞ / k be a ℤ p -extension and A n the p-Sylow subgroup of the ideal class group of k n , where k n is the n th layer of k ∞ / k . Then there exist integers λ = λ ( k ∞ / k ) ≥ 0 , μ = μ ( k ∞ / k ) ≥ 0 , ν = ν ( k ∞ / k ) , and n₀ ≥ 0...

Baireness of C k ( X ) for ordered X

Michael Granado, Gary Gruenhage (2006)

Commentationes Mathematicae Universitatis Carolinae

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We show that if X is a subspace of a linearly ordered space, then C k ( X ) is a Baire space if and only if C k ( X ) is Choquet iff X has the Moving Off Property.

Guidance properties of a cylindrical defocusing waveguide

Oldřich John, Charles A. Stuart (1994)

Commentationes Mathematicae Universitatis Carolinae

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We discuss the propagation of electromagnetic waves of a special form through an inhomogeneous isotropic medium which has a cylindrical symmetry and a nonlinear dielectric response. For the case where this response is of self-focusing type the problem is treated in [1]. Here we continue this study by dealing with a defocusing dielectric response. This tends to inhibit the guidance properties of the medium and so guidance can only be expected provided that the cylindrical stratification...