Email this article Generators of Groups and Lie Algebras of the Form F/[N,N]
- Authors: Krasnikov A.F.1
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Affiliations:
- Omsk State University
- Issue: Vol 215, No 4 (2016)
- Pages: 517-528
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/237640
- DOI: https://doi.org/10.1007/s10958-016-2856-4
- ID: 237640
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Abstract
Let F be a free product of nontrivial groups Ai, i ∈ I, and a free group G, and let N be a normal subgroup of F such that N ∩ Ai = 1, i ∈ I. We establish necessary and sufficient conditions for a given element of the group F/[N,N] to belong to the subgroup generated by a given set of elements of F/[N,N] and necessary and sufficient conditions for a given finite set of elements of F/[N,N] to be a set of generators of F/[N,N]. Similar results are obtained for Lie algebras. Bibliography: 10 titles.
About the authors
A. F. Krasnikov
Omsk State University
Author for correspondence.
Email: phomsk@mail.ru
Russian Federation, 55-A, pr. Mira, Omsk, 644077
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