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Lobachevskii Journal of Mathematics

, Volume 39, Issue 1, pp 93–96 | Cite as

Some Properties of Elements of the Group F/[N,N]

  • A. F. Krasnikov
Article

Abstract

Let F be a free group with basis {x j |jJ}; N a normal subgroup of F. For a given element n of N we describe an elements D l (n), where D l : Z(F) → Z(F) (lJ) 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, r1 d is in the normal closure of r2 d 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, rN(k) and F/RN(k) is torsion free then F/RN(k+1) is torsion free.

Keywords and phrases

Group ring solvable group 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Omsk State UniversityOmskRussia

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