Solution of Belousov's problem
| dc.creator | Akivis, Maks A. | |
| dc.creator | Goldberg, Vladislav V. | |
| dc.date | 2000-10-17 | |
| dc.date.accessioned | 2026-07-07T04:38:06Z | |
| dc.date.available | 2026-07-07T04:38:06Z | |
| dc.description | 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 $n$-quasigroups for any n \geq 3. | |
| dc.description | AMS-LaTeX, 7 pages | |
| dc.identifier | https://arxiv.org/abs/math/0010175 | |
| dc.identifier | http://arxiv.org/abs/math/0010175 | |
| dc.identifier | Discuss. Math. Gen. Algebra Appl. 51 (2001) no. 1 193-203 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60151 | |
| dc.subject | Group Theory | |
| dc.subject | 20N05 (Primary), 53A60 (Secondary) | |
| dc.title | Solution of Belousov's problem | |
| dc.type | text |