  Let $V$ be a faithful $G$-module for a finite group $G$ and let $p$ be a
prime dividing $|G|$. An orbit $v^G$ for the action of $G$ on $V$ is
$p$-regular if $|v^G|_p=|G:\bC_G(v)|_p=|G|_p$. Zhang asks the following
question in \cite{Zhang}. Assume that a finite solvable group $G$ acts
faithfully and irreducibly on a vector space $V$ over a finite field $\FF$. If
$G$ has a $p$-regular orbit for every prime $p$ dividing $|G|$, is it true that
$G$ will have a regular orbit on $V$? In \cite{LuCao}, L\"{u} and Cao construct
an example showing that the answer to this question is no, however the example
itself is not correct. In this paper, we study Zhang's question in detail. We
construct examples showing that the answer to this question is no in general.
We also prove the following result. Assume a finite solvable group $G$ of odd
order acts faithfully and irreducibly on a vector space $V$ over a field of odd
characteristic. If $G$ has a $p$-regular orbit for every prime $p$ dividing
$|G|$, then $G$ will have a regular orbit on $V$.
