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Torsion-free groups isomorphic to all of their non-nilpotent subgroups

Part of: Special aspects of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

Patrizia Longobardi ,
Mercede Maj ,
Howard Smith  and
James Wiegold
Patrizia Longobardi
Affiliation:
Dipartimento di Matematica e Informatica, via S. Allende, 84081 Baronissi, Italy e-mail: longobar@matna2.dma.unina.it e-mail: maj@matna2.dma.unina.it
Mercede Maj
Affiliation:
Bucknell University, Lewisburg PA 17837, USA e-mail: howsmith@bucknell.edu
Howard Smith
Affiliation:
School of Mathematics, Cardiff University, Cardiff CF24 4Y, Wales e-mail: smajw@cardiff.ac.uk
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Abstract

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The main result is that every torsion-free locally nilpotent group that is isomorphic to each of its nonnilpotent subgroups is nilpotent, that is, a torsion-free locally nilpotent group G that is not nilpotent has a non-nilpotent subgroup H that is not isomorphic to G.

Keywords

torsion-freelocally nilpotent groups

MSC classification

Secondary: 20F19: Generalizations of solvable and nilpotent groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 71 , Issue 3 , December 2001 , pp. 339 - 348
Copyright
Copyright © Australian Mathematical Society 2001

References

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