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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)

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
Full Text: DOI
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