论文标题
新的陀螺群的构建及其子gyrogroup的结构
Construction of New Gyrogroups and the Structure of their Subgyrogroups
论文作者
论文摘要
假设$ g $是具有二进制操作$ \ otimes $的群体。如果操作$ \ otimes $具有左份身份，则对$（g，\ otimes）$据说是gyrogroup，g $中的每个元素$ a \ in g $ in左右，陀螺仪法律和陀螺仪法律，并且在$ g $中满足了左循环属性。在本文中，提出了一种构造旧陀螺群的方法，并提供了这些陀螺群的副群的结构。由于这项工作，提出了五个$ 2- $ 2- $的订单$ 2^n $，$ n \ geq 3 $。还提出了一些公开问题。
Suppose that $G$ is a groupoid with binary operation $\otimes$. The pair $(G,\otimes)$ is said to be a gyrogroup if the operation $\otimes$ has a left identity, each element $a \in G$ has a left inverse and the gyroassociative law and the left loop property are satisfied in $G$. In this paper, a method for constructing new gyrogroups from old ones is presented and the structure of subgyrogroups of these gyrogroups are also given. As a consequence of this work, five $2-$gyrogroups of order $2^n$, $n\geq 3$, are presented. Some open questions are also proposed.
