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Bull. Korean Math. Soc. 2013; 50(2): 667-674
Printed March 31, 2013
https://doi.org/10.4134/BKMS.2013.50.2.667
Copyright © The Korean Mathematical Society.
Compatibility in certain quasigroup homogeneous space
Bokhee Im and Ji-Young Ryu
Chonnam National University, Chonnam National University
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.
Keywords: quasigroup, Latin square, action matrix, quasigroup action, homogeneous space, approximate symmetry, intercalate, compatibility
MSC numbers: Primary 20N05; Secondary 05C69, 20B99
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