Abstract.
The paper identifies the class of all permutation representations of a given finite quasigroup as a covariety of coalgebras. Each permutation representation decomposes as a sum of homomorphic images of homogeneous spaces. For a group, permutation representations in the present sense specialise to the classical concept. Burnside's Lemma, with a new proof, is extended from groups to quasigroups.
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Received March 13, 2002; accepted in final form September 18, 2002.
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ID="h1"This paper was written while the author was a guest of the Institute of Mathematics and Information Sciences at Warsaw University of Technology, on Faculty Professional Development Assignment from Iowa State University.
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Smith, J. A coalgebraic approach to quasigroup permutation representations. Algebra univers. 48, 427–438 (2002). https://doi.org/10.1007/s000120200010
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DOI: https://doi.org/10.1007/s000120200010