Geodesic
On verbal subgroups in finite and profinite groups
Algebra and discrete mathematics, Tome 14 (2012) no. 1, pp. 1-13

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $w$ be a multilinear commutator word. In the present paper we describe recent results that show that if $G$ is a profinite group in which all $w$-values are contained in a union of finitely (or in some cases countably) many subgroups with a prescribed property, then the verbal subgroup $w(G)$ has the same property as well. In particular, we show this in the case where the subgroups are periodic or of finite rank.
Keywords: Profinite groups, verbal subgroups, coverings, multilinear commutators. 
@article{ADM_2012_14_1_a1,
     author = {Cristina Acciarri and Pavel Shumyatsky},
     title = {On verbal subgroups in finite and profinite groups},
     journal = {Algebra and discrete mathematics},
     pages = {1--13},
     publisher = {mathdoc},
     volume = {14},
     number = {1},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2012_14_1_a1/}
}
TY  - JOUR
AU  - Cristina Acciarri
AU  - Pavel Shumyatsky
TI  - On verbal subgroups in finite and profinite groups
JO  - Algebra and discrete mathematics
PY  - 2012
SP  - 1
EP  - 13
VL  - 14
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADM_2012_14_1_a1/
LA  - en
ID  - ADM_2012_14_1_a1
ER  - 
%0 Journal Article
%A Cristina Acciarri
%A Pavel Shumyatsky
%T On verbal subgroups in finite and profinite groups
%J Algebra and discrete mathematics
%D 2012
%P 1-13
%V 14
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADM_2012_14_1_a1/
%G en
%F ADM_2012_14_1_a1
Cristina Acciarri; Pavel Shumyatsky. On verbal subgroups in finite and profinite groups. Algebra and discrete mathematics, Tome 14 (2012) no. 1, pp. 1-13. http://geodesic.mathdoc.fr/item/ADM_2012_14_1_a1/