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July, 2008 On the verbal width of finitely generated pro-$p$ groups
Andrei Jaikin-Zapirain
Rev. Mat. Iberoamericana 24(2): 617-630 (July, 2008).


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.


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Andrei Jaikin-Zapirain . "On the verbal width of finitely generated pro-$p$ groups." Rev. Mat. Iberoamericana 24 (2) 617 - 630, July, 2008.


Published: July, 2008
First available in Project Euclid: 11 August 2008

zbMATH: 1158.20012
MathSciNet: MR2459206

Primary: 20E18
Secondary: 22E35

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

Rights: Copyright © 2008 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.24 • No. 2 • July, 2008
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