论文标题
建造所有订单的所有陀螺仪最多31
Construction of All Gyrogroups of Orders at most 31
论文作者
论文摘要
Gyrogroup是与有史以来发现的群体最接近的代数结构。它具有一个二进制操作$ \ star $，其中包含一个身份元素，因此每个元素都有一个倒数。此外，对于此结构的每个元素的每对$（a，b）$，都有一个属性属性的自动形态$ \ gyr {a，b} {} $，并满足了该属性，该属性满足并满足了左环属性。由于每个Gyrogroup都是左BOL环路，因此Burn的一些结果暗示着所有订单的gyrogroup $ P，2p $和$ p^2 $都是组。本文的目的是对8、12、15、18、20、21和28的订单的陀螺群进行分类。
The gyrogroup is the closest algebraic structure to the group ever discovered. It has a binary operation $\star$ containing an identity element such that each element has an inverse. Furthermore, for each pair $(a,b)$ of elements of this structure there exists an automorphism $\gyr{a,b}{}$ with this property that left associativity and left loop property are satisfied. Since each gyrogroup is a left Bol loop, some results of Burn imply that all gyrogroups of orders $p, 2p$ and $p^2$ are groups. The aim of this paper is to classify gyrogroups of orders 8, 12, 15, 18, 20, 21, and 28.
