与消失子群V（G）有关的中心列
A Central series associated with the vanishing off subgroup V(G)
摘要：
推广了Lewis关于与消失子群相联系的中心列的结果.我们把PDMATHAMN的消失子群写成PDMATHAMM，把这个中心列中的项写成$V_{i}=[V_{i-1},G]$。Lewis证明了存在正整数$n$使得如果$V_{3} < G_{3}$，则$|G:V_{1}|=|G':V_{2}|^{2}=p^{2n}$。让$D_{3}/V_{3} = C_{G/V_{3}}(G'/V_{3})$。他还表明，如果$V_{3} < G_{3}$，那么要么是$|G:D_{3}|=p^{n}$，要么是$D_{3}=V_{1}$。我们证明，如果$V_{i} <G_{i}$对于$i\ge 4,$，其中$G_{i}$是$G$的下中心列中的$i$项，则$|G_{i-1}:V_{i-1}|=|G:D_{3}|.$
英文摘要：
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 $|G:V_{1}|=|G':V_{2}|^{2}=p^{2n}$. 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 $G_{i}$ is the $i$-th term in the lower central series of $G$, then $|G_{i-1}:V_{i-1}|=|G:D_{3}|.$
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