Let be a prime. It is proved that a non-trivial word from a free group has finite width in every finitely generated pro- group if and only if . Also it is shown that any word has finite width in a compact -adic group.
Cite this article
Andrei Jaikin-Zapirain, On the verbal width of finitely generated pro- groups. Rev. Mat. Iberoam. 24 (2008), no. 2, pp. 617–630DOI 10.4171/RMI/549