Paper read at the Symposium on Categorical Algebra and Topology University of Cape Town 29 June—3 July 1981

NILPOTENT GROUPS AND ABELIANIZATION

Published in: Quaestiones Mathematicae
Volume 6 , issue 1-3 , 1983 , pages: 143–155

DOI: 10.1080/16073606.1983.9632297

Author(s): Peter Hilton , Switzerland

Keywords: 20F18 , 55P60

Abstract

We study the question of what properties of nilpotent groups are shared by their abelianizations. We identify two such properties—that of being a π-torsion group, where π is a family of primes, and that of having q^th roots, for some prime q. We use these properties to provide simplified proofs of the following theorems in the localization of nilpotent groups.

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