Use this URL to cite or link to this record in EThOS:  https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.343780 
Title:  Model subgroups of finite soluble groups  
Author:  Carr, Ben 
ISNI:
0000 0001 3520 8678


Awarding Body:  University of Warwick  
Current Institution:  University of Warwick  
Date of Award:  1998  
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Abstract:  
In this thesis we begin the study of finite groups possessing a model subgroup, where a model subgroup H of a finite group G is defined to be a subgroup satisfying 〖1H〗^(↑G)=∑_(x∊∕π(G))▒X We show that a finite nilpotent group possesses a model subgroup if and only if it is abelian and that a Frobenius group with Frobenius complement C and Frobenius kernel N possesses a model subgroup if and only if (a) N is elementary abelian of order r". (b) C is cyclic of order (r" — 1 )/(rd — 1), for some d dividing n. (c) The finite field F=Frn has an additive abelian subgroup HF of order rd satisfying NormF/K(HF) =K, where K=Frd. We then go on to conjecture that a finite soluble group G possessing a model subgroup is either metabelian or has a normal subgroup N such that G/N is a Frobenius group with cyclic Frobenius complement of order 2" +1 and elementary abelian Frobenius kernel of order 22". We consider a series of cases that need to be excluded in order to prove the conjecture and present some examples that shed light on the problems still to be overcome.


Supervisor:  Not available  Sponsor:  Science and Engineering Research Council  
Qualification Name:  Thesis (Ph.D.)  Qualification Level:  Doctoral  
EThOS ID:  uk.bl.ethos.343780  DOI:  Not available  
Keywords:  QA Mathematics  
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