Some properties of Neumann quasigroups

Abstract

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.

7 pages