Homology of free Lie powers and torsion in groups
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- Stöhr, R. Israel J. Math. (1993) 84: 65. doi:10.1007/BF02761691
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LetG be a group that is given by a free presentationG=F/R, and letγ4R 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/[γ4R,F] can be identified with the homology groupRγ6(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.