Some remarks on Lie dimension subgroups. (English) Zbl 0761.20004

Gupta, Narain; Srivastava, J. B.

J. Algebra 143, No. 1, 57-62 (1991).

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

Keywords:

augmentation ideal; integral group ring; Lie products; Lie dimension subgroup; lower central series; dimension subgroup conjecture; Lie dimension subgroup conjecture; commutators

References:

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