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- W4288278890 abstract "It is well known that the set of values of a lower central word in a group $G$ need not be a subgroup. For a fixed lower central word $gamma_r$ and for $pge 5$, Guralnick showed that if $G$ is a finite $p$-group such that the verbal subgroup $gamma_r(G)$ is abelian and 2-generator, then $gamma_r(G)$ consists only of $gamma_r$-values. In this paper we extend this result, showing that the assumption that $gamma_r(G)$ is abelian can be dropped. Moreover, we show that the result remains true even if $p=3$. Finally, we prove that the analogous result for pro-$p$ groups is true." @default.
- W4288278890 created "2022-07-28" @default.
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- W4288278890 date "2019-07-26" @default.
- W4288278890 modified "2023-09-29" @default.
- W4288278890 title "Lower central words in finite $p$-groups" @default.
- W4288278890 doi "https://doi.org/10.48550/arxiv.1907.11479" @default.
- W4288278890 hasPublicationYear "2019" @default.
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