Georgian Mathematical Journal 09 (2002), No. 4, 703--708
Copyright Heldermann Verlag 2002
A Magnus-Witt Type Isomorphism for Non-Free Groups
G. Ellis
Mathematics Department, National University, Galway, Ireland
We use the theory of nonabelian derived functors to prove that certain Baer invariants of a group G are torsion when G has torsion second integral homology. We use this result to show that if such a group has torsion-free abelianisation then the Lie algebra formed from the quotients of the lower central series of G is isomorphic to the free Lie algebra on Gab. We end the paper with some related remarks about precrossed modules and partial Lie algebras.
Keywords: Baer invariants, nonabelian derived functors, precrossed module, partial Lie albebra, Peiffer commutator.
MSC: 20E14, 20F40; 20J06 18G50
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