Characters of finite quasigroups. VI: Critical examples and doubletons
type: Item
instance of: scholarly article
title: Characters of finite quasigroups. VI: Critical examples and doubletons
zbMATH Open document ID: 0704.20056
DOI: 10.1016/S0195-6698(13)80126-6
author: Elsie Sterbin Gottlieb
published in: European Journal of Combinatorics
publication date: 1990-01-01T00:00:00Z
review text: [Part V see ibid. 10, No.5, 449-456 (1989; Zbl 0679.20059).] The aim of this paper is to present critical examples of scheme character tables which are demonstrably not quasigroup character tables. Immediate sporadic examples are offered by the character tables of the schemes given by strongly regular graphs with 26 vertices. The main task of the note is to present members of an infinite family of examples, such as \[ \left[\begin{matrix} 1 & 1 & 1 \\ \sqrt{7} & 1/3\sqrt{7} & -1/3\sqrt{7} \\ 2\sqrt{5} & -1/3\sqrt{5} & 2/15\sqrt{5}\end{matrix}\right] \] of scheme character tables which are demonstrably not quasigroup character tables. This is done in Theorem: Let r be an even integer greater than 4. Then the character table of the Johnson scheme \(J(r,2)\) is not a quasigroup character table.
Mathematics Subject Classification ID: 20N05
Mathematics Subject Classification ID: 05E30
Mathematics Subject Classification ID: 20C99
zbMATH DE Number: 4154750
zbMATH Keywords: scheme character tables
zbMATH Keywords: quasigroup character tables
zbMATH Keywords: strongly regular graphs
zbMATH Keywords: Johnson scheme
reviewed by: C. Pereira da Silva
MaRDI profile type: Publication
cites work: Characters of finite quasigroups
cites work: Characters of finite quasigroups. II: Induced characters
cites work: Characters of finite quasigroups. III: Quotients and fusion
cites work: Characters of finite quasigroups. IV: Products and superschemes
cites work: Characters of finite quasigroups. V: Linear characters
cites work: Quasigroups. II
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: Current research on algebraic combinatorics. Supplements to our book, Algebraic combinatorics I
cites work: Character tables of the association schemes of finite orthogonal groups acting on the nonisotropic points
cites work: A Class of Simple Moufang Loops
cites work: S-rings over loops, right mapping groups and transversals in permutation groups
cites work: Q3749248
cites work: Q3781251
cites work: Loop transversals and the centralizer ring of a permutation group
cites work: On t-homogeneous permutation sets
cites work: Q3218140
cites work: Q5707657
cites work: Classification and Analysis of Partially Balanced Incomplete Block Designs with Two Associate Classes
cites work: On a Characterization of the Triangular Association Scheme
cites work: The Uniqueness of the Triangular Association Scheme
cites work: The Johnson graph \(J(d,r)\) is unique if \((d,r)\neq (2,8)\)
cites work: Q4039780
cites work: Q3995195
full work available at URL: s0195-6698(13)80126-6
OpenAlex ID: W2009625036
description: scientific article; zbMATH DE number 4154750