On a theorem of J. E. Olson and an application. (Vanishing sums in finite abelian \(p\)-groups)
type: Item
instance of: scholarly article
title: On a theorem of J. E. Olson and an application. (Vanishing sums in finite abelian \(p\)-groups)
zbMATH Open document ID: 0908.11010
author: G. Troi
author: Umberto Zannier
published in: Finite Fields and their Applications
publication date: 1999-03-07T00:00:00Z
review text: Let \(p\) be a prime number and let \(P\) be the direct product of cyclic groups of order \(p^{n_1}, \cdots, p^{n_s}\). Let \(S_1, \cdots, S_k\) be sets of integers noncongruent modulo \(p\). Assume \(| S_1|+ \cdots+ | S_k| \geq p^{n_1}+ \cdots+ p^{n_s}-s+1\). The authors show that for every sequence \(g_1, \cdots, g_k\) of elements of \(A\), there are \(s_i\in (S_i\cup \{0\})\) such that \(s_1g_1+\cdots +s_kg_k=0\) and \(| s_1| +\cdots +| s_k| >0\).
Mathematics Subject Classification ID: 11B83
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 1199969
zbMATH Keywords: zero sums
zbMATH Keywords: finite abelian \(p\)-groups
reviewed by: Yahya Ould Hamidoune
MaRDI profile type: Publication
full work available at URL: ffta.1996.0179
OpenAlex ID: W2015884119
cites work: Q5581789
cites work: A combinatorial problem on finite Abelian groups. I
cites work: Q3997223
cites work: Q5631207
DOI: 10.1006/FFTA.1996.0179
description: scientific article; zbMATH DE number 1199969