Revista Matemática Iberoamericana


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Volume 24, Issue 2, 2008, pp. 617–630
DOI: 10.4171/RMI/549

On the verbal width of finitely generated pro-$p$ groups

Andrei Jaikin-Zapirain[1]

(1) Departamento de Matemáticas, Universidad Autónoma de Madrid, Ciudad Universitaria de Cantoblanco, 28049, MADRID, SPAIN

Let $p$ be a prime. It is proved that a non-trivial word $w$ from a free group $F$ has finite width in every finitely generated pro-$p$ group if and only if $w\not \in (F^\prime)^{p} F^{\prime\prime}$. Also it is shown that any word $w$ has finite width in a compact $p$-adic group.

Keywords: pro-p group, verbal subgroup, verbal width, p-adic analytic group

Jaikin-Zapirain Andrei: On the verbal width of finitely generated pro-$p$ groups. Rev. Mat. Iberoamericana 24 (2008), 617-630. doi: 10.4171/RMI/549