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A Magnus-Witt type isomorphism for non-free groups. (English) Zbl 1048.20017
Let $$\gamma_nG$$ denote the lower central series of the group $$G$$ and $$\Gamma G=\bigoplus_{n\geq 1}\gamma_nG/\gamma_{n+1}G$$ be the Lie algebra of quotients of the $$\gamma_nG$$. Let $$L(G_{ab})$$ be the free Lie algebra on the Abelian group $$G_{ab}=G/\gamma_2G$$. The author proves that certain Baer invariants of $$G$$ are torsion when $$G$$ has torsion second integral homology. This result is used to show that if $$G$$ has torsion-free Abelianisation then $$\Gamma G$$ is isomorphic to $$L(G_{ab})$$.

MSC:
 20F14 Derived series, central series, and generalizations for groups 20F40 Associated Lie structures for groups 20J05 Homological methods in group theory 18G50 Nonabelian homological algebra (category-theoretic aspects)
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