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We generalize Lewis's result about a central series associated with thevanishing 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 provedthat there exists a positive integer $n$ such that if $V_{3} < G_{3}$, then$|G:V_{1}|=|G':V_{2}|^{2}=p^{2n}$. Let $D_{3}/V_{3} = C_{G/V_{3}}(G'/V_{3})$.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 $i\ge 4,$ where $G_{i}$ isthe $i$-th term in the lower central series of $G$, then$|G_{i-1}:V_{i-1}|=|G:D_{3}|.$

A Central series associated with the vanishing off subgroup V(G)