## A coalgebraic approach to quasigroup permutation representations.(English)Zbl 1068.20070

The paper is devoted to permutation representations of finite quasigroups. The class of all permutation representations of a given finite quasigroup is identified with a covariety of coalgebras. Each permutation representation decomposes as a sum of homomorphic images of homogeneous spaces. For groups, permutation representations in the sense presented specialize to the classical concept. Also Burnside’s Lemma is extended from groups to quasigroups.

### MSC:

 20N05 Loops, quasigroups 20C15 Ordinary representations and characters 08C05 Categories of algebras 16W30 Hopf algebras (associative rings and algebras) (MSC2000)
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