• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.667-674
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• 2013

Considering a special double-cover Q of the symmetric group of degree 3, we show that a proper non-regular approximate symmetry occurs from its quasigroup homogeneous space. The weak compatibility of any two elements of Q is completely characterized in any such quasigroup homogeneous space of degree 4.

• Honam Mathematical Journal
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• v.41 no.3
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• pp.595-607
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• 2019

We consider quasigroups $Q({\Gamma})$ obtained as certain double covers of the symmetric group $S_3$ of degree 3, for directed graphs ${\Gamma}$ on the vertex set $S_3$. We completely characterize the strong compatibility of elements of $Q({\Gamma})$ for any quasigroup nonuniform homogeneous space of degree 4. For such homogeneous spaces, we classify all the strong and weak compatibility graphs of $Q({\Gamma})$.