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A Magnus–Witt Type Isomorphism for Non-Free Groups

A Magnus–Witt Type Isomorphism for Non-Free Groups 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Georgian Mathematical Journal de Gruyter

A Magnus–Witt Type Isomorphism for Non-Free Groups

Georgian Mathematical Journal , Volume 9 (4) – Dec 1, 2002

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Publisher
de Gruyter
Copyright
© Heldermann Verlag
ISSN
1072-947X
eISSN
1072-9176
DOI
10.1515/GMJ.2002.703
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Georgian Mathematical Journalde Gruyter

Published: Dec 1, 2002

Keywords: Baer invariants; nonabelian derived functors; precrossed module; partial Lie albebra; Peiffer commutator

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