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- W4295161213 abstract "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 $ige 4,$ where $G_{i}$ is the $i$-th term in the lower central series of $G$, then $|G_{i-1}:V_{i-1}|=|G:D_{3}|.$" @default.
- W4295161213 created "2022-09-11" @default.
- W4295161213 creator A5021626938 @default.
- W4295161213 date "2012-09-13" @default.
- W4295161213 modified "2023-09-26" @default.
- W4295161213 title "A Central series associated with the vanishing off subgroup V(G)" @default.
- W4295161213 doi "https://doi.org/10.48550/arxiv.1209.2886" @default.
- W4295161213 hasPublicationYear "2012" @default.
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