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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 𝐺 𝑎𝑏 . We end the paper with some related remarks about precrossed modules and partial Lie algebras.
Georgian Mathematical Journal – de Gruyter
Published: Dec 1, 2002
Keywords: Baer invariants; nonabelian derived functors; precrossed module; partial Lie albebra; Peiffer commutator
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