Difference bases in cyclic groups-Reference-Cited by-同舟云学术

Difference bases in cyclic groups

Published:2019-05 Issue:05 Volume:18 Page:1950081
ISSN:0219-4988
Container-title:Journal of Algebra and Its Applications
language:en
Short-container-title:J. Algebra Appl.

Author:

Banakh Taras O.¹²,Gavrylkiv Volodymyr M.³

Affiliation:

1. Faculty of Mechanics and Mathematics, Ivan Franko National University of Lviv 1, Universytetska St., Lviv 79000, Ukraine

2. Institute of Mathematics, Jan Kochanowski University in Kielce, Kielce, Poland

3. Faculty of Mathematics and Computer Science, Vasyl Stefanyk Precarpathian National University, 57, Shevchenka St., Ivano-Frankivsk 76018, Ukraine

Abstract

A subset [Formula: see text] of an Abelian group [Formula: see text] is called a difference basis of [Formula: see text] if each element [Formula: see text] can be written as the difference [Formula: see text] of some elements [Formula: see text]. The smallest cardinality [Formula: see text] of a difference basis [Formula: see text] is called the difference size of [Formula: see text] and is denoted by [Formula: see text]. We prove that for every [Formula: see text] the cyclic group [Formula: see text] of order [Formula: see text] has difference size [Formula: see text]. If [Formula: see text] (and [Formula: see text]), then [Formula: see text] (and [Formula: see text]). Also, we calculate the difference sizes of all cyclic groups of cardinality [Formula: see text].

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219498819500816

Reference21 articles.

1. The Difference Between Consecutive Primes, II

2. Algebra in the superextensions of twinic groups

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