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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
##### Keywords:
loop; Bernstein algebras; quasigroups; identities; iterated squaring
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