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Title: The influence of nilpotent subgroups on the nilpotent length and derived length of a finite group
Author: Jones, Graham Robert
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 1983
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In 1969, Dade showed that the nilpotent length of a finite soluble group is bounded in terms of the composition length of a Carter subgroup. The main aim of this thesis is to prove a dual result to this involving nilpotent injectors instead of Carter subgroups: namely, we prove the following theorem. THEOREM. Let E be a nilpotent injector of the finite soluble group G. Suppose that E can be generated by m elements, and that G has nilpotent length 1. Then 1 ≤ ∑m + 3. Three other (similar) bounds are also proved.. All four results are consequences of two theorems concerning the representation theory of a soluble group over a finite field.
Supervisor: Not available Sponsor: Sussex European Research Centre
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics