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Extensions of a problem of Paul Erdös on groups

Part of: Structure and classification of infinite or finite groups Special aspects of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

John C. Lennox  and
James Wiegold
John C. Lennox
Affiliation:
Department of Mathmatics, University College, Cardiff, Wales
James Wiegold
Affiliation:
Department of Mathmatics, University College, Cardiff, Wales
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Abstract

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The main results are as follows. A finitely generated soluble group G is polycyclic if and only if every infinite set of elements of G contains a pair generating a polycyclic subgroup; and the same result with “polycyclic” replaced by “coherent”.

MSC classification

Secondary: 20F16: Solvable groups, supersolvable groups 20E25: Local properties
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 31 , Issue 4 , December 1981 , pp. 459 - 463
Copyright
Copyright © Australian Mathematical Society 1981

References

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