关于一类回转群的注记

摘要：

在\cite{1}中，一类回转群$(G,\odot)$已经与某些群$(G,\cdot)$相关联。给出了$(G,\odot)$是回转交换的一个充要条件.我们还证明了在适当的假设下，以$2$ -Engel群为中心的两个有限群同构当且仅当它们的相关回转群同构.

英文摘要：

In \cite{1}, a class of gyrogroups $(G,\odot)$ has been associated to certain groups $(G,\cdot)$. We give a necessary and sufficient condition for $(G,\odot)$ to be gyrocommutative. We also prove that under a suitable assumption two finite groups central by a $2$-Engel group are isomorphic if and only if their associated gyrogroups are isomorphic.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。