On profinite groups with word values covered by nilpotent subgroups

Let N stand for the class of nilpotent groups or one of its well-known generalizations. For a multilinear commutator word w and a profinite group G we show that w ( G ) is finite-by- N if and only if the set of w values in G is covered by countably many finite-by- N subgroups. Earlier this was known...

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Bibliographic Details
Published in:Israel journal of mathematics 2018-06, Vol.226 (2), p.993-1008
Main Authors: Detomi, Eloisa, Morigi, Marta, Shumyatsky, Pavel
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Group Theory and Generalizations
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Subgroups
Theoretical
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Summary:Let N stand for the class of nilpotent groups or one of its well-known generalizations. For a multilinear commutator word w and a profinite group G we show that w ( G ) is finite-by- N if and only if the set of w values in G is covered by countably many finite-by- N subgroups. Earlier this was known only in the case where w = x or w = [ x , y ].
ISSN:0021-2172
1565-8511
DOI:10.1007/s11856-018-1720-2