CMA Research Report

MRR03-006

Groups with strong Wielandt length two

Abstract:  The strong Wielandt subgroup of a group is the intersection of the centralizers of its nilpotent subnormal sections. It is non-trivial in any finite group and thus gives rise to a series which we may regard as a generalisation of the upper central series of nilpotent groups. In this note we give a characterisation of finite soluble groups with strong Wielandt length at most two, which may be viewed as an extension of the classification of T-groups due to Gaschütz et al.

AMS Classification:  20D35
Date:  18 September 2003

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