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Homology of free Lie powers and torsion in groups

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Abstract

LetG be a group that is given by a free presentationG=F/R, and letγ4 R denote the fourth term of the lower central series of R. We show that ifG has no elements of order 2, then the torsion subgroup of the free central extensionF/[γ4 R,F] can be identified with the homology groupR γ6(G, ℤ/2ℤ). This is a consequence of our main result which refers to the homology ofG with coefficients in Lie powers of relation modules.

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Authors and Affiliations

  1. Department of Mathematics, UMIST, M60 1QD, Manchester, England

    Ralph Stöhr

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  1. Ralph Stöhr
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Stöhr, R. Homology of free Lie powers and torsion in groups. Israel J. Math. 84, 65–87 (1993). https://doi.org/10.1007/BF02761691

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