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Representations of metabelian groups satisfying the minimal condition for normal subgroups

Published online by Cambridge University Press:  17 April 2009

Howard L. Silcock
Howard L. Silcock
Affiliation:
Department of Pure Mathematics, University of Adelaide, Adelaide, South Australia.
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Abstract

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A question of John S. Wilson concerning indecomposable representations of metabelian groups satisfying the minimal condition for normal subgroups is answered negatively, by means of an example. It is shown that such representations need not be irreducible, even when the group being represented is an extension of an elementary abelian p–group by a quasicyclic q–group of the type first described by V.S. Čarin, and the characteristic of the field is a prime distinct from both p and q. This implies that certain techniques used in the study of metabelian groups satisfying the minimal condition for normal subgroups are not available for the corresponding class of soluble groups of derived length 3.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 14 , Issue 2 , April 1976 , pp. 267 - 278
Copyright
Copyright © Australian Mathematical Society 1976

References

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