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Finite groups admitting a fixedpointfree automorphism
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Rowley, Peter J. (1975) Finite groups admitting a fixedpointfree automorphism. PhD thesis, University of Warwick.

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Official URL: http://webcat.warwick.ac.uk/record=b1747660~S15
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.
Item Type:  Thesis or Dissertation (PhD)  

Subjects:  Q Science > QA Mathematics  
Library of Congress Subject Headings (LCSH):  Finite groups, Fixed point theory, Automorphisms  
Official Date:  June 1975  
Dates: 


Institution:  University of Warwick  
Theses Department:  Mathematics Institute  
Thesis Type:  PhD  
Publication Status:  Unpublished  
Supervisor(s)/Advisor:  Hawkes, Trevor O.  
Sponsors:  Science Research Council (Great Britain)  
Extent:  vii, 137 leaves  
Language:  eng 
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