Abstract

A finite group G is called a $\text{DCI}$-group if every two isomorphic Cayley digraphs over G are Cayley isomorphic, i.e. their connection sets are conjugate by a group automorphism. We prove that the group $C_4\times C_p^2,$ where p is a prime, is a $\text{DCI}$-group if and only if $p\ne 2.$

中文翻译：

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C 4×C p 2群的Cayley同构性质

摘要

有限群G称为a$\text{DCI}$-如果G上的每两个同构Cayley有向图是Cayley同构，即它们的连接集通过组自同构而共轭。我们证明该小组$C_4\times C_p^2，$其中p是素数，是a$\text{DCI}$-group当且仅当 $p\ne 2。$