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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:
[1] Gupta, N, The dimension subgroup conjecture, Bull. London math. soc., 22, 453-456, (1990) · Zbl 0721.20001
[2] Gupta, N; Levin, F, On the Lie ideals of a ring, J. algebra, 81, 225-231, (1983) · Zbl 0514.16024
[3] Hurley, T.C; Sehgal, S.K, The Lie dimension subgroup conjecture, J. algebra, 143, 46-56, (1991) · Zbl 0761.20003
[4] Levin, F; Sehgal, S.K, On Lie nilpotent group rings, J. pure appl. algebra, 37, 33-39, (1985) · Zbl 0576.16009
[5] Rips, E, On the fourth integer dimension subgroups, Israel J. math., 12, 342-346, (1972) · Zbl 0267.20018
[6] Sandling, R, The dimension subgroup problem, J. algebra, 21, 216-231, (1972) · Zbl 0233.20001
[7] \scR. K. Sharma and J. B. Srivastava, Lie centrally metabelian group group rings, J. Algebra, to appear. · Zbl 0788.16019
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