Some properties of Neumann quasigroups

Natalia N. Didurik, Victor A. Shcherbacov

Published 2018-09-19Version 1

Any Neumann quasigroup $(Q, \cdot)$ (quasigroup with Neumann identity $ x \cdot(yz \cdot yx) = z$ is called Neumann quasigroup) can be presented in the form $x\cdot y = x-y$, where $(Q, +)$ is an abelian group. Automorphism group of Neumann quasigroup coincides with the group $Aut(Q, +)$. Any Schweizer quasigroup (quasigroup with Schweizer identity $xy \cdot xz = zy$ is called Schweizer quasigroup) is a Neumann quasigroup and vice versa. Any Neumann quasigroup is a GA-quasigroup.