论文标题
组的Cayley同构属性$ C^5_2 \ Times C_P $
The Cayley isomorphism property for the group $C^5_2\times C_p$
论文作者
论文摘要
如果$ g $超过$ g $的两个cayley digraphs是同构的，并且仅当它们的连接集由组自动形态结合时，则有限的$ g $被称为dci group。我们证明，当$ p $是prime的组$ C_2^5 \ times c_p $时，当且仅当$ p \ neq 2 $时。与先前获得的结果一起，这意味着$ g $ $ g $ 32p $，其中$ p $是prime，当时仅当$ p \ neq 2 $和$ g \ g \ cong c_2^5 \ times c_p $。
A finite group $G$ is called a DCI-group if two Cayley digraphs over $G$ are isomorphic if and only if their connection sets are conjugate by a group automorphism. We prove that the group $C_2^5\times C_p$, where $p$ is a prime, is a DCI-group if and only if $p\neq 2$. Together with the previously obtained results, this implies that a group $G$ of order $32p$, where $p$ is a prime, is a DCI-group if and only if $p\neq 2$ and $G\cong C_2^5\times C_p$.
