# Solution of Belousov's problem

```@article{Akivis2000SolutionOB,
title={Solution of Belousov's problem},
author={Maks A. Akivis and Vladislav V. Goldberg},
journal={arXiv: Group Theory},
year={2000}
}```
• Published 17 October 2000
• Mathematics
• arXiv: Group Theory
The authors prove that a local \$n\$-quasigroup defined by the equation x_{n+1} = F (x_1, ..., x_n) = [f_1 (x_1) + ... + f_n (x_n)]/[x_1 + ... + x_n], 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 \neq j, are not both linear homogeneous, or these functions are linear homogeneous but f_i (x_i)/x_i \neq f_j (x_j)/x_j. This gives a solution of Belousov's problem to construct examples of irreducible \$n…
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