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• W2556079624 abstract "Let $$mathcal {N}$$ be the class of pronilpotent groups, or the class of locally nilpotent profinite groups, or the class of strongly locally nilpotent profinite groups. It is proved that a profinite group G is finite-by- $$mathcal {N}$$ if and only if G is covered by countably many $$mathcal {N}$$ -subgroups. The commutator subgroup $$G'$$ is finite-by- $$mathcal {N}$$ if and only if the set of all commutators in G is covered by countably many $$mathcal {N}$$ -subgroups. Here, a group is strongly locally nilpotent if it generates a locally nilpotent variety of groups. According to Zelmanov, a locally nilpotent group is strongly locally nilpotent if and only if it is n-Engel for some positive n." @default.
• W2556079624 created "2016-11-30" @default.
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• W2556079624 date "2016-11-15" @default.
• W2556079624 modified "2023-10-06" @default.
• W2556079624 title "On groups covered by locally nilpotent subgroups" @default.
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• W2556079624 doi "https://doi.org/10.1007/s10231-016-0627-y" @default.
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