Splittings of infinite Abelian groups
type: Item
instance of: scholarly article
title: Splittings of infinite Abelian groups
zbMATH Open document ID: 0589.20035
DOI: 10.1007/BF02189919
author: Steve Galovich
author: Jack Goldfeather
author: Stan Seltzer
author: Kay Smith
published in: Aequationes Mathematicae
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/137120
review text: Minkowski's problem concerning tilings of Euclidean space by cubes was solved by \textit{G. Hajós} [see Math. Z. 47, 427-467 (1941; Zbl 0025.25401)]. He reduced Minkowski's geometrical problem to a problem in finite group theory involving a factorization of a finite group. The principal result of the present paper is a prime decomposition theorem for splittings of \(\mathbb{Z}\) (the additive group of integers).
Mathematics Subject Classification ID: 20K99
Mathematics Subject Classification ID: 52C17
Mathematics Subject Classification ID: 20K27
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 3946457
zbMATH Keywords: tilings of Euclidean space
zbMATH Keywords: factorization
zbMATH Keywords: prime decomposition theorem
zbMATH Keywords: splittings of \(\mathbb{Z}\)
reviewed by: József Dénes
MaRDI profile type: Publication
cites work: Factoring by subsets
cites work: Algebraic Tiling
OpenAlex ID: W4250977044
description: scientific article; zbMATH DE number 3946457