Characters of finite quasigroups VII: Permutation characters

Kenneth Johnson, J. D.H. Smith

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Each homogeneous space of a quasigroup affords a representation of the Bose- Mesner algebra of the association scheme given by the action of the multiplication group. The homogeneous space is said to be faithful if the corresponding representation of the Bose-Mesner algebra is faithful. In the group case, this definition agrees with the usual concept of faithfulness for transitive permutation representations. A permutation char- acter is associated with each quasigroup permutation representation, and specialises appropriately for groups. However, in the quasigroup case the character of the homoge- neous space determined by a subquasigroup need not be obtained by induction from the trivial character on the subquasigroup. The number of orbits in a quasigroup permu- tation representation is shown to be equal to the multiplicity with which its character includes the trivial character.

Original languageEnglish (US)
Pages (from-to)265-273
Number of pages9
JournalCommentationes Mathematicae Universitatis Carolinae
Volume45
Issue number2
StatePublished - Jan 1 2004

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Quasigroup
Permutation
Homogeneous Space
Bose-Mesner Algebra
Permutation Representation
Faithful
Trivial
Association Scheme
Proof by induction
Multiplicity
Multiplication
Orbit
Character

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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Characters of finite quasigroups VII : Permutation characters. / Johnson, Kenneth; Smith, J. D.H.

In: Commentationes Mathematicae Universitatis Carolinae, Vol. 45, No. 2, 01.01.2004, p. 265-273.

Research output: Contribution to journalArticle

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