Difference bases in finite Abelian groups

Banakh, Taras and Gavrylkiv, Volodymyr: Difference bases in finite Abelian groups. Acta scientiarum mathematicarum, (85) 1-2. pp. 119-137. (2019)

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Abstract

A subset B of a group G is called a difference basis of G if each element g ∈ G can be written as the difference g = ab−1 of some elements a, b ∈ B. The smallest cardinality |B| of a difference basis B ⊂ G is called the difference size of G and is denoted by ∆[G]. The fraction ð[G] := ∆[G]/ p |G| is called the difference characteristic of G. Using properties of the Galois rings, we prove recursive upper bounds for the difference sizes and characteristics of finite Abelian groups. In particular, we prove that for a prime number p ≥ 11, any finite Abelian p-group G has difference characteristic ð[G] < p−1 √p−3 · supk∈N ð[Cpk ] < 2 · √p−1 √p−3 . Also we calculate the difference sizes of all Abelian groups of cardinality less than 96.

Item Type: Article
Journal or Publication Title: Acta scientiarum mathematicarum
Date: 2019
Volume: 85
Number: 1-2
Page Range: pp. 119-137
ISSN: 2064-8316
DOI: https://doi.org/10.14232/actasm-017-586-x
Uncontrolled Keywords: Matematika
Additional Information: Bibliogr.: p. 136-137. ; összefoglalás angol nyelven
Official URL: http://www.acta.hu
Date Deposited: 2019. Sep. 25. 10:06
Last Modified: 2019. Sep. 25. 10:06
URI: http://acta.bibl.u-szeged.hu/id/eprint/62136

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