Characters of Finite Quasigroups IV: Products and Superschemes

K. W. Johnson, J. D.H. Smith

Research output: Contribution to journalArticle

17 Scopus citations

Abstract

For finite loops (as for finite groups), the character table of a direct product is the tensor product of the character tables of the direct factors. This is no longer true for quasigroups. Although non-ℨ and ℨ-quasigroups may have the same character table, the character table of Q × Q determines whether a finite non-empty quasigroup Q lies in ℨ or not. A combinatorial interpretation of the tensor square of a quasigroup character table is obtained, in terms of superschemes, a higherdimensional extension of the concept of association scheme.

Original languageEnglish (US)
Pages (from-to)257-263
Number of pages7
JournalEuropean Journal of Combinatorics
Volume10
Issue number3
DOIs
StatePublished - Jan 1 1989

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics

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