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Title: Finite groups admitting a fixed-point-free 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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The content of this thesis is a proof of the following theorem: Let G be a finite group admitting a fixed-point- free coprime automorphism α of order rst, where r,s and t are distinct primes and rst is a non-Fermat number. Then G is soluble. A non-Fermat number is defined to be one which is not divisible by an integer of the form 2m+1 (m >1) ; there are infinitely many non-Fermat 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, fixed-point-freely 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 well-known conjecture: let G be a finite group admitting the automorphism group A fixed-point-freely and, if A is non-cyclic; 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:  DOI: Not available
Keywords: QA Mathematics