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IMI/Publicaţii/BASM/Ediţii/BASM n.2(81), 2016/

On spectrum of medial T2-quasigroups

Authors: A. V. Scerbacova, Şcerbacov Victor

Abstract

There exist medial $T_2$-quasigroups of any order of the form $$2^{\,k_1} 3^{k_2} 5^{k_3} 11^{k_4} 17^{k_5} 23^{k_6} 53^{k_7} 59^{k_8} 83^{k_9} 101^{k_{10}} p_1^{\alpha_1} p_2^{\alpha_2} \dots p_m^{\alpha_m}, $$ where $k_1\geq 2$, $k_2, \dots, k_{10} \geq 1$, $p_i$ are prime numbers of the form $6t+1$, $\alpha_i \in \mathbb N$, $i\in \{1 , \dots, m\}$. Some other results on $T_2$-quasigroups are given.

A. V. Scerbacova
Gubkin Russian State Oil and Gas University
Leninsky Prospect, 65, Moscow 119991
Russia
E-mail:

V. A. Shcherbacov
Institute of Mathematics and Computer Science
Academy of Sciences of Moldova
Academiei str. 5, MD−2028 Chisinau
Moldova
E-mail:

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