On the nilpotent length of a finite group with a frobenius group of automorphisms

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2013

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Öğüt, Elif

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Let G be a finite group admitting a Frobenius group FH of automorphisms with kernel F and complement H. Assume that the order of G and FH are relatively prime and H acts regularly on the fixed point subgroup of F in G. It is proved in this thesis that the nilpotent length of G is less than or equal to the sum of the nilpotent length of the commutator group of G and F with 1 and the nilpotent length of the commutator group of G and F is equal to the nilpotent length of the fixed point subgroup of H in the commutator group of G and F.

Subject Keywords

Group theory., Solvable groups., Frobenius groups., Nilpotent Lie groups., Automorphisms.

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http://etd.lib.metu.edu.tr/upload/12615949/index.pdf
https://hdl.handle.net/11511/22814

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Graduate School of Natural and Applied Sciences, Thesis

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Citation Formats

E. Öğüt, “On the nilpotent length of a finite group with a frobenius group of automorphisms,” Ph.D. - Doctoral Program, Middle East Technical University, 2013.