  We give several equivalent characterization of aperiodicity of an element on
locally compact group $G$, and give an intuition for "How strong does the
aperiodicity of an element affect the existence of hypercyclic weighted
translation operators?". In fact, if $a$ is an aperiodic element in $G$, then
there exists a mixing, chaotic and frequently hypercyclic weighted translation
$T_{a,w}$ on $L^p(G)$.
