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Title: Characters of finite quasigroups VII: permutation characters (English)
Author: Johnson, K. W.
Author: Smith, J. D. H.
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 45
Issue: 2
Year: 2004
Pages: 265-273
Category: math
Summary: 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 character is associated with each quasigroup permutation representation, and specialises appropriately for groups. However, in the quasigroup case the character of the homogeneous 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 permutation representation is shown to be equal to the multiplicity with which its character includes the trivial character. (English)
Keyword: quasigroup
Keyword: association scheme
Keyword: permutation character
MSC: 05E30
MSC: 20C99
MSC: 20N05
idZBL: Zbl 1101.20037
idMR: MR2075274
Date available: 2009-05-05T16:44:57Z
Last updated: 2012-04-30
Stable URL:
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