On Schur rings over cyclic groups
type: Item
instance of: scholarly article
title: On Schur rings over cyclic groups
zbMATH Open document ID: 0962.20002
DOI: 10.1007/BF02773471
author: Ka Hin Leung
author: Shing Hing Man
published in: Israel Journal of Mathematics
publication date: 1999-01-21T00:00:00Z
review text: The notion of Schur ring was first studied by Schur and later by \textit{H. Wielandt} [see his book `Finite permutation groups', Academic Press, New York (1964; Zbl 0138.02501)]. Schur rings have applications in algebraic combinatorics. The aim of this paper is to show that there are simple ways to construct Schur rings over finite cyclic groups from Schur rings over smaller cyclic groups. To this end, the notions of dot product and wedge product on Schur rings are introduced. The second goal is to show that for all except one type of Schur rings over a finite cyclic group \(G\), they can be constructed by using a dot product or wedge product on Schur rings over smaller cyclic groups.
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 05E30
zbMATH DE Number: 1216496
zbMATH Keywords: Schur rings
zbMATH Keywords: finite cyclic groups
zbMATH Keywords: dot products
zbMATH Keywords: wedge products
reviewed by: Yakov Berkovich
MaRDI profile type: Publication
cites work: The structure of Schur rings over cyclic groups
cites work: On Schur rings over cyclic groups. II
cites work: The structure of rational Schur rings over cyclic groups
cites work: On the structure of basic sets of Schur rings over cyclic groups
cites work: Q5286393
cites work: On Schur-rings which define a proper character theory on finite groups
cites work: On construction and identification of graphs. With contributions by A. Lehman, G. M. Adelson-Velsky, V. Arlazarov, I. Faragev, A. Uskov, I. Zuev, M. Rosenfeld and B. Weisfeiler
cites work: Q5512231
description: scientific article; zbMATH DE number 1216496