There are many possible ways to de. ne Moufang element. We show that the traditional definition is not the most felicitious - for instance, the set of all Moufang elements in an arbitrary loop, qua the traditional definition, need not form a subloop. We offer a new definition of Moufang element that ensures that the set of all Moufang elements in an arbitrary loop is a subloop. Moreover, this definition is "maximally algebraic" with respect to autotopisms. We also give an application of this new definition by showing that a flexible A-element in an inverse property loop is, in fact, a Moufang element, thus sharpening a well-known result of Kinyon, Kunen, and the present author [6]. Finally, we prove that divisible, Moufang groupoids are Moufang loops, thus sharpening a result of Kunen [9], one of the first computer-generated proofs in loop theory.
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机译：有很多可能的方法。 ne Moufang元素。我们证明了传统定义并不是最合适的-例如，在传统定义的任意循环中，所有Moufang元素的集合都不需要形成子循环。我们提供了对Moufang元素的新定义，以确保任意循环中所有Moufang元素的集合都是一个子循环。而且，就自拓扑而言，该定义是“最大代数”。通过显示逆属性循环中的柔性A元素实际上是一个Moufang元素，我们还给出了这个新定义的应用，从而增强了Kinyon，Kunen和本作者的知名结果[6]。 。最后，我们证明了可分割的，Moufang类群是Moufang环，从而提高了Kunen [9]的结果，Kunen [9]是循环理论中最早的计算机生成的证明之一。
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