engleski

On medial-like identities

The description of the quasigroups that satisfy the identities of the form (a.b).(c.d) = (\pi(a).\pi(b)).(\pi(c).\pi(d)), where \pi is a certain permutation on {; ; ; a, b, c, d}; ; ; , is given. Those quasigroups include internally medial (ab.cd=ac.bd), externally medial (ab.cd=db.ca) and palindromic (ab.cd=dc.ba) quasigroups. There are six identities that are the equivalents of commutativity, and fourteen identities are the equivalents of commutative mediality.

quasigroup; medial

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