Splitting groups of prime order
type: Item
instance of: scholarly article
title: Splitting groups of prime order
zbMATH Open document ID: 0624.20036
DOI: 10.1007/BF01836152
author: Sherman Stein
published in: Aequationes Mathematicae
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/137203
review text: Let M be a finite set of nonzero integers and let G be a finite abelian group. A subset S of G is a splitting set for M if each element in G-\(\{\) \(0\}\) is uniquely expressible in the form ms, \(m\in M\), \(s\in S\) and \(| M| | S| =| G-\{0\}|\). Also M is said to split G. This concept is connected with tiling Euclidean space by translates of certain star bodies. The paper examines splittings primarily in the special case \(M=\{1,2,...,k\}\), where k is a positive integer. In particular in the case where G is a group of prime order the author relates such splittings to Newton sums.
Mathematics Subject Classification ID: 20K01
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 52C17
Mathematics Subject Classification ID: 52C07
zbMATH DE Number: 4012895
zbMATH Keywords: finite abelian group
zbMATH Keywords: splitting set
zbMATH Keywords: tiling Euclidean space
zbMATH Keywords: group of prime order
zbMATH Keywords: splittings
reviewed by: Rodica Covaci
MaRDI profile type: Publication
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OpenAlex ID: W1999905240
description: scientific article; zbMATH DE number 4012895