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On homotopies of finite \(n\)-quasigroups. (Russian) Zbl 0744.20060
Finite \(n\)-quasigroups are considered. A homotopy of an \(n\)-quasigroup \(B\) onto an \(n\)-quasigroup \(A\) is said to be non-trivial, if \(| B| > | A| > 1\). The author finds a condition for the existence non-trivial homotopies of an \(n\)-quasigroup onto another one, and describes all \(n\)-quasigroups being a homotopy pre-image of a given \(n\)-quasigroup. He describes all homotopies of quasigroups which are isotopic to groups.
MSC:
20N15 \(n\)-ary systems \((n\ge 3)\)
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