Jones, Graham Robert (1983) The influence of nilpotent subgroups on the nilpotent length and derived length of a finite group. PhD thesis, University of Warwick.

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Abstract

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.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Nilpotent groups, Solvable groups, Finite groups
Official Date:	1983
Dates:	Date Event 1983 Submitted
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Hawkes, Trevor O.,1936-
Sponsors:	Sussex European Research Centre
Extent:	vii, 122 leaves
Language:	eng

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