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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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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:  DOI: Not available
Keywords: QA Mathematics