Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.594904
Title: Radical properties of certain group algebras
Author: Knott, Roger Peter
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 1970
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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.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.594904  DOI: Not available
Keywords: QA Mathematics
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