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Solution of Belousov's problem

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Akivis M., Goldberg V.

Discussiones Mathematicae - General Algebra and Applications

2001

tom 21

nr 1

93-103

The authors prove that a local n-quasigroup defined by the equation $x_{n+1} = F(x₁,...,xₙ) = (f₁(x₁) + ... + fₙ(xₙ))/(x₁ + ... + xₙ)$, where $f_{i}(x_{i})$, i,j = 1,...,n, are arbitrary functions, is irreducible if and only if any two functions $f_{i}(x_{i})$ and $f_{j}(x_{j})$, i ≠ j, are not both linear homogeneous, or these functions are linear homogeneous but $f_{i}(x_{i})/x_{i} ≠ f_{j}(x_{j})/x_{j}$. This gives a solution of Belousov's problem to construct examples of irreducible n-quasigroups for any n ≥ 3.

Ograniczanie wyników

1 Discussiones Mathematicae - General Algebra and Applications

1 Akivis M.

1 Goldberg V.

1 2001

Wyniki wyszukiwania

Solution of Belousov's problem