In this manuscript, we generalize Lewis’s result about a central series associated with the vanishing off subgroup. We write
$V_{1}=V(G)$
for the vanishing off subgroup of
$G$
, and
$V_{i}=[V_{i-1},G]$
for the terms in this central series. Lewis proved that there exists a positive integer
$n$
such that if
$V_{3}<G_{3}$
, then
$|G\,:\,V_{1}|=|G^{\prime }\,:\,V_{2}|^{2}=p^{2n}$
. Let
$D_{3}/V_{3}=C_{G/V_{3}}(G^{\prime }/V_{3})$
. He also showed that if
$V_{3}<G_{3}$
, then either
$|G\,:\,D_{3}|=p^{n}$
or
$D_{3}=V_{1}$
. We show that if
$V_{i}<G_{i}$
for
$i\geqslant 4$
, where
$G_{i}$
is the
$i$
-th term in the lower central series of
$G$
, then
$|G_{i-1}\,:\,V_{i-1}|=|G\,:\,D_{3}|$
.