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A conjecture of Lennox and Wiegold concerning supersoluble 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

J. R. J. Groves
J. R. J. Groves
Affiliation:
Department of MathematicsUniversity of MelbourneParkville, Vic., 3052, Australia
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Abstract

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We prove a conjecture of Lennox and Wiegold that a finitely generated soluble group, in which every infinite subset contains two elements generating a supersoluble group, is finite-by-supersoluble.

MSC classification

Secondary: 20F16: Solvable groups, supersolvable groups 20E25: Local properties
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 35 , Issue 2 , October 1983 , pp. 218 - 220
Copyright
Copyright © Australian Mathematical Society 1983

References

[1]Lennox, John C. and Wiegold, James, ‘Extensions of a problem of Paul Erdös on groups’, J. Austral. Math Soc. Ser. A 31 (1981), 459–463.CrossRefGoogle Scholar
[2]Neumann, B. H., ‘A problem of Paul Erdös on groups’, J. Austral Math. Soc. Ser. A 21 (1976), 467–472.Google Scholar
[3]Wehrfritz, B. A. F., Infinite linear groups (Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 76, Springer, Berlin 1973).CrossRefGoogle Scholar