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Soluble groups isomorphic to their non-nilpotent subgroups

Part of: Special aspects of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

Howard Smith  and
James Wiegold
Howard Smith
Affiliation:
Bucknell UniversityLewisburg PA 17837USA e-mail: howsmith@bucknell.edu
James Wiegold
Affiliation:
School of Mathematics Cardiff UniversitySenghennydd Road Cardiff CF24 4YN Wales e-mail: wiegoldj@cardiff.ac.uk
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Abstract

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A group G belongs to the class W if G has non-nilpotent proper subgroups and is isomorphic to all of them. The main objects of study are the soluble groups in W that are not finitely generated. It is proved that there are no torsion-free groups of this sort, and a reasonable classification is given in the finite rank case.

MSC classification

Secondary: 20F19: Generalizations of solvable and nilpotent groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 67 , Issue 3 , December 1999 , pp. 399 - 411
Copyright
Copyright © Australian Mathematical Society 1999

References

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