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Plenary stable quasigroups. (English) Zbl 0734.20032
Let the classes \(V_ k\) of quasigroups be defined by the identities (*) \(a^{[k]}=a^{[k+1]}\), \(k\geq 1\). The author presents some properties of a quasigroup Q (called plenary stable) satisfying (*). So, some results are obtained for quasigroups in which the operation of iterated squaring always leads to stability irrespective of the initial element.

MSC:
20N05 Loops, quasigroups
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