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Some examples of finiteness conditions in centre-by-metabelian 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 Mathematics University of MelbourneParkville, Victoria 3053, Australia
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Abstract

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Centre-by-metabelian groups with the maximal condition for normal subgroups are exhibited which (a) are residually finite but have quotient groups which are not residually finite; and (b) have all quotients residually finite but are not abelian-by-polycyclic.

MSC classification

Secondary: 20F16: Solvable groups, supersolvable groups 20E26: Residual properties and generalizations; residually finite groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 38 , Issue 2 , April 1985 , pp. 171 - 174
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Segal, D., ‘On the residual simplicity of certain modules’, Proc. London Math. Soc. (3) 34 (1977), 327–353.CrossRefGoogle Scholar