, Volume 84, Issue 1-2, pp 65-87

Homology of free Lie powers and torsion in groups

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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.