Use this URL to cite or link to this record in EThOS:  https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.471099 
Title:  Finite groups admitting a fixedpointfree automorphism  
Author:  Rowley, Peter J. 
ISNI:
0000 0001 3538 8277


Awarding Body:  University of Warwick  
Current Institution:  University of Warwick  
Date of Award:  1975  
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Abstract:  
The content of this thesis is a proof of the following theorem: Let G be a finite group admitting a fixedpoint free coprime automorphism α of order rst, where r,s and t are distinct primes and rst is a nonFermat number. Then G is soluble. A nonFermat number is defined to be one which is not divisible by an integer of the form 2m+1 (m >1) ; there are infinitely many nonFermat numbers which are the product of three distinct primes. G is said to admit A, a subgroup of Aut G, the automorphism group of G, fixedpointfreely if and only if Cg(A) = {g ε G I a(g) = g for all a ε A } = {1}. The result provides a solution to part of this wellknown conjecture: let G be a finite group admitting the automorphism group A fixedpointfreely and, if A is noncyclic; also assume [A] is coprime to [G]. Then G is soluble.


Supervisor:  Not available  Sponsor:  Science Research Council  
Qualification Name:  Thesis (Ph.D.)  Qualification Level:  Doctoral  
EThOS ID:  uk.bl.ethos.471099  DOI:  Not available  
Keywords:  QA Mathematics  
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