On the verbal width of finitely generated pro-$p$ groups
Rev. Mat. Iberoamericana, Tome 24 (2008) no. 2, p. 617-630 / Harvested from Project Euclid
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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.
Publié le : 2008-04-15
Classification:  pro-$p$ group,  verbal subgroup,  verbal width,  $p$-adic analytic group,  20E18,  22E35 
@article{1218475356,
     author = {Jaikin-Zapirain
,  
Andrei},
     title = {On the verbal width of finitely generated pro-$p$ groups},
     journal = {Rev. Mat. Iberoamericana},
     volume = {24},
     number = {2},
     year = {2008},
     pages = { 617-630},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1218475356}
}

Jaikin-Zapirain
,  
Andrei. On the verbal width of finitely generated pro-$p$ groups. Rev. Mat. Iberoamericana, Tome 24 (2008) no. 2, pp.  617-630. http://gdmltest.u-ga.fr/item/1218475356/