On spectrum of medial $T_2$-quasigroups

A. V. Scerbacova ; V. A. Shcherbacov

Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2016), pp. 143-154.

Résumé

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 $k_1\ge 2$, $k_2,\dots ,k_{10}\ge 1$, $p_i$ 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.

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