On the Proof of a Theorem of Pálfy

Abstract

Pálfy proved that a group $G$ is a CI-group if and only if $\vert G\vert = n$ where either $\gcd(n,\varphi(n)) = 1$ or $n = 4$, where $\varphi$ is Euler's phi function. We simplify the proof of "if $\gcd(n,\varphi(n)) = 1$ and $G$ is a group of order $n$, then $G$ is a CI-group".