Rowley, Peter J. (1975) Finite groups admitting a fixed-point-free automorphism. PhD thesis, University of Warwick.

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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 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.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Finite groups, Fixed point theory, Automorphisms
Official Date:	June 1975
Dates:	Date Event June 1975 Submitted
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Publication Status:	Unpublished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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