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

Published online by Cambridge University Press:  09 April 2009

Patrizia Longobardi
Affiliation:
Dipartimento di Matematica e Informatica, via S. Allende, 84081 Baronissi, Italy e-mail: [email protected] e-mail: [email protected]
Mercede Maj
Affiliation:
Bucknell University, Lewisburg PA 17837, USA e-mail: [email protected]
Howard Smith
Affiliation:
School of Mathematics, Cardiff University, Cardiff CF24 4Y, Wales e-mail: [email protected]
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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.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2001

References

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