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For a fixed lower central word $\\gamma_r$ and for $p\\ge 5$, 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 $p=3$. 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