Geodesic
Quasigroup automorphisms and symmetric group characters
Commentationes Mathematicae Universitatis Carolinae, Tome 51 (2010) no. 2, pp. 279-286.

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The automorphisms of a quasigroup or Latin square are permutations of the set of entries of the square, and thus belong to conjugacy classes in symmetric groups. These conjugacy classes may be recognized as being annihilated by symmetric group class functions that belong to a $\lambda$-ideal of the special $\lambda$-ring of symmetric group class functions.
Classification : 05B15, 05E10, 19A22, 20C30, 20N05
Keywords: Latin square; quasigroup; automorphism; $\lambda$-ring 
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Kerby, Brent; Smith, Jonathan D. H. Quasigroup automorphisms and symmetric group characters. Commentationes Mathematicae Universitatis Carolinae, Tome 51 (2010) no. 2, pp. 279-286. http://geodesic.mathdoc.fr/item/CMUC_2010__51_2_a12/