Neumann拟群的一些性质
Some properties of Neumann quasigroups
摘要：
任何Neumann拟群$(Q, \cdot)$（具有Neumann恒等式的拟群$ x \cdot(yz \cdot yx) = z$称为Neumann拟群）都可以表示为$x\cdot y = x-y$的形式，其中$(Q, +)$是阿贝尔群。Neumann拟群的自同构群与群$Aut(Q, +)$重合。任何Schweizer拟群（具有Schweizer恒等式$xy \cdot xz = zy$的拟群称为Schweizer拟群）是Neumann拟群，反之亦然。任何Neumann拟群都是GA-拟群。
英文摘要：
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.
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