Exact sequences in homology of multiplicative Lie rings and a new version of Stallings' theorem

We show that the non-abelian tensor product of nilpotent, solvable and Engel multiplicative Lie rings is nilpotent, solvable and Engel, respectively. The six term exact sequence in homology of multiplicative Lie rings is obtained. We also prove a new version of Stallings' theorem.

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Bibliographic Details
Published in:Journal of pure and applied algebra 2018-07, Vol.222 (7), p.1786-1802
Main Authors: Donadze, G., Inassaridze, N., Ladra, M., Vieites, A.M.
Format: Article
Language:English
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Summary:We show that the non-abelian tensor product of nilpotent, solvable and Engel multiplicative Lie rings is nilpotent, solvable and Engel, respectively. The six term exact sequence in homology of multiplicative Lie rings is obtained. We also prove a new version of Stallings' theorem.
ISSN:0022-4049
1873-1376
DOI:10.1016/j.jpaa.2017.08.006