Fitting Height of a Finite Group with a Metabelian Group of Automorphisms |
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Authors: | Emerson de Melo |
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Institution: | 1. Department of Mathematics , University of Brasilia , Brasilia , Brazil e.f.melo@mat.unb.br |
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Abstract: | Let M = FH be a finite group that is a product of a normal abelian subgroup F and an abelian subgroup H. Assume that all elements in M?F have prime order p, and F has at most one subgroup of order p. Examples of such groups are dihedral groups for p = 2 and the semidirect product of a cyclic group F by a group H of prime order p such that C F (H) = 1 or |C F (H)| =p and C F/C F (H)(H) = 1. Suppose that M acts on a finite group G in such a manner that C G (F) = 1. We prove that the Fitting height h(G) of G is at most h(C G (H))+ 1. Moreover, the Fitting series of C G (H) coincides with the intersection of C G (H) with the Fitting series of G. |
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Keywords: | Automorphisms Fixed-point-free Fitting height |
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