This is a survey of results from the rich theory of medial and more general quasigroups and its close connection with the geometry of point-reflections. The emphasis is on questions regarding the simplest axiomatization, in the sense of the minimal number of variables appearing in the identtties, on dependence or independence of axioms, and on representation theorems in the style of Toyoda.

中文翻译：

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点反射和拟群的几何

这是对丰富的中间和更一般拟群理论及其与点反射几何的紧密联系的结果的一项调查。重点是关于最简单的公理化的问题，即恒等式中出现的变量数量最少，公理的依赖性或独立性以及丰田定式的表示定理。