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Some remarks on Lie dimension subgroups. (English) Zbl 0761.20004
We use the notation of the preceding review Zbl 0761.20003.
In this paper the authors show that $$D_{[n]}(G)\neq \gamma_ n(G)$$ for $$9\leq n\leq 13$$. This result combined with the Hurley-Sehgal result now shows that for $$n\geq 9$$, $$D_{[n]}(G)\neq \gamma_ n(G)$$. The authors’ theorem requires substantial computations with commutators. They also show that for $$n\geq 2$$, $$D_{4n}(G)\nsubseteq\gamma_{3n+1}(G)$$ in the course of proving the above.
Reviewer: E.Spiegel (Storrs)

##### MSC:
 20C07 Group rings of infinite groups and their modules (group-theoretic aspects) 20F14 Derived series, central series, and generalizations for groups 20F40 Associated Lie structures for groups 20E07 Subgroup theorems; subgroup growth 20F12 Commutator calculus 16S34 Group rings
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##### References:
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