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http://dx.doi.org/10.5831/HMJ.2019.41.3.595

STRONG COMPATIBILITY IN CERTAIN QUASIGROUP NONUNIFORM HOMOGENEOUS SPACES OF DEGREE 4  

Im, Bokhee (Department of Mathematics, Chonnam National University)
Ryu, Ji-Young (Department of Mathematics, Chonnam National University)
Publication Information
Honam Mathematical Journal / v.41, no.3, 2019 , pp. 595-607 More about this Journal
Abstract
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 $Q({\Gamma})$.
Keywords
quasigroup; quasigroup action; homogeneous space; intercalate; strongly compatible; compatibility graph; compatibility;
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Times Cited By KSCI : 1  (Citation Analysis)
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