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\(n\)-ary loops with invertibility property. (Russian) Zbl 0744.20061
Author’s summary: It is given a new definition of the \(n\)-loops with the invertibility property when the arity is greater then two as loops and the principal isostope of this loop is the initial loop. There are studied the properties of the inverse translations, the dependence of the inversion matrix on the identity element, the pseudoautomorphisms, the kernel and center and also some properties of autotopies of this family of loops. The corresponding examples are constructed.
MSC:
20N15 \(n\)-ary systems \((n\ge 3)\)
20N05 Loops, quasigroups
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