Knott, Roger Peter (1970) Radical properties of certain group algebras. PhD thesis, University of Warwick.

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Abstract

In this thesis we are concerned with the following problem: if F is a field and G a group, what conditions must be imposed on F and G so that the group algebra of G over F is S semi-simple? Here, S is one of the ring properties, nil, nilpotent, right-quasi-regu1ar or B-regular.

In the first few chapters we survey the known conditions where S is nil, nilpotent or right-quasi-regular. In a later chapter we shall show that if F is any field, the group algebra of G over F is right-quasi-regular semi-simple if G belongs to a certain class of torsion-free generalised soluble groups. We then study a generalisation of the group algebra, namely the twisted group algebra, and determine conditions on F and G when S is nil, nilpotent or right-quasi-regular. Finally we assume that S is B-regularity. We then determine conditions on F and G for the group algebra to be B-regular semi-simple when G belongs to a certain class of generalised nilpotent groups.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Group algebras
Official Date:	1970
Dates:	Date Event 1970 Submitted
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Extent:	100 leaves
Language:	eng

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