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The wielandt series of metabelian groups

Published online by Cambridge University Press:  17 April 2009

C.J.T. Wetherell
C.J.T. Wetherell
Affiliation:
Mathematical Sciences Institute, ANU Canberra, ACT 0200, Australia
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Abstract

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The Wielandt subgroup of a group is the intersection of the normalisers of its subnormal subgroups. It is non-trivial in any finite group and thus gives rise to a series whose length provides a measure of the complexity of the group's subnormal structure. In this paper results of Ormerod concerning the interplay between the Wielandt series and upper central series of metabelian p-groups, p odd, are extended to the class of all odd order metabelian groups. These extensions are formulated in terms of a natural generalization of the upper central series which arises from Casolo's strong Wielandt subgroup, the intersection of the centralisers of a group's nilpotent subnormal sections.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 67 , Issue 2 , April 2003 , pp. 267 - 276
Copyright
Copyright © Australian Mathematical Society 2003

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