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Infinite metacyclic groups and their non-abelian tensor squares

Published online by Cambridge University Press:  20 January 2009

James R. Beuerle  and
Luise-Charlotte Kappe
James R. Beuerle
Affiliation:
Department of Mathematics, Elon College, Elon College, NC 27244, USA (jbeuerle@elon.edu)
Luise-Charlotte Kappe
Affiliation:
Department of Mathematical Sciences, SUNY at Binghamton, Binghamton, NY 13902–6000, USA (menger@math.binghamton.edu)
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Abstract

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In this paper we classify all infinite metacyclic groups up to isomorphism and determine their non-abelian tensor squares. As an application we compute various other functors, among them are the exterior square, the symmetric product, and the second homology group for these groups. We show that an infinite non-abelian metacyclic group is capable if and only if it is isomorphic to the infinite dihedral group

Keywords

non-abelian tensor productsmetacyclic groupscapabilityhomological functors
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 43 , Issue 3 , October 2000 , pp. 651 - 662
Copyright
Copyright © Edinburgh Mathematical Society 2000

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