On the index of fixed point subgroup

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index.pdf

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2011

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Türkan, Erkan Murat

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Let G be a finite group and A be a subgroup of Aut(G). In this work, we studied the influence of the index of fixed point subgroup of A in G on the structure of G. When A is cyclic, we proved the following: (1) [G,A] is solvable if this index is squarefree and the orders of G and A are coprime. (2) G is solvable if the index of the centralizer of each x in H-G is squarefree where H denotes the semidirect product of G by A. Moreover, for an arbitrary subgroup A of Aut(G) whose order is coprime to the order of G, we showed that when G is solvable, then the Fitting length f([G,A]) of [G,A] is bounded above by the number of primes (counted with multiplicities) dividing the index of fixed point subgroup of A in G and this bound is best possible.

Subject Keywords

Fixed point theory.

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http://etd.lib.metu.edu.tr/upload/12613522/index.pdf
https://hdl.handle.net/11511/21116

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Graduate School of Natural and Applied Sciences, Thesis

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Citation Formats

E. M. Türkan, “On the index of fixed point subgroup,” Ph.D. - Doctoral Program, Middle East Technical University, 2011.