Some Properties of Elements of the Group F/[N,N]
- Authors: Krasnikov A.F.1
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Affiliations:
- Omsk State University
- Issue: Vol 39, No 1 (2018)
- Pages: 93-96
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/200976
- DOI: https://doi.org/10.1134/S1995080218010171
- ID: 200976
Cite item
Abstract
Let F be a free group with basis {xj|j ∈ J}; N a normal subgroup of F. For a given element n of N we describe an elements Dl(n), where Dl: Z(F) → Z(F) (l ∈ J) are the Fox derivations of the group ring Z(F). If r1, r2 are an elements of F/[N,N] and, for some positive integer d, r1d is in the normal closure of r2d in F/[N,N], then r1 is in the normal closure of r2 in F/[N,N]. Let F/N be a soluble group; r an element of F, R the normal closure of r in F. If, for some positive integer k, r ∉ N(k) and F/RN(k) is torsion free then F/RN(k+1) is torsion free.
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About the authors
A. F. Krasnikov
Omsk State University
Author for correspondence.
Email: phomsk@mail.ru
Russian Federation, pr.Mira 55-A, Omsk, 644077