Abstract
We use an analogue of Gluskin–Hosszú theorem for strongly dependent finite n-ary semigroups to prove an analogue of Post coset theorem. We show that in fact these theorems are equivalent. Thus it turns our that the case of n-ary semigroups is fully similar to the case of n-groups.
Note: Originally published in Diskretnaya Matematika (2019) 31, №2, 152–157 (in Russian).
References
[1] Post E. L., “Polyadic groups”, Trans. Amer. Math. Soc., 48:2 (1940), 208–350.10.1090/S0002-9947-1940-0002894-7Search in Google Scholar
[2] Gluskin L. M., “Positional operatives”, Mat. Sb., 68(110):3 (1965), 444–472 (in Russian).Search in Google Scholar
[3] Hosszu M., “On the explicit form of n-group operations”, Publ. Math., 10:1–4 (1963), 88–92.10.5486/PMD.1963.10.1-4.11Search in Google Scholar
[4] Gal’fmak A. M., Vorob’fyev G.N. On Post–Gluskin–Hosszu theorem, Problemy fiziki, matematiki i tekhniki, 2013, №1(14), 55–59 (in Russian).Search in Google Scholar
[5] Cheremushkin A. V., “Analogues of Gluskin–Hosszú and Malyshev theorems for strongly dependent n-ary operations”, Discrete Math. Appl., 29:5 (2019), 295–302.10.1515/dma-2019-0027Search in Google Scholar
© 2020 Walter de Gruyter GmbH, Berlin/Boston
