Characters of Finite Quasigroups IV

Products and Superschemes

Kenneth Johnson, J. D.H. Smith

Research output: Contribution to journalArticle

17 Citations (Scopus)

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

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Character Table
Quasigroup
Association Scheme
Direct Product
Tensor Product
Finite Group
Tensor
Character

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics

Cite this

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Characters of Finite Quasigroups IV : Products and Superschemes. / Johnson, Kenneth; Smith, J. D.H.

In: European Journal of Combinatorics, Vol. 10, No. 3, 01.01.1989, p. 257-263.

Research output: Contribution to journalArticle

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