Finite groups and Lie rings with a metacyclic Frobenius group of automorphisms

@inproceedings{Khukhro2013FiniteGA,
  title={Finite groups and Lie rings with a metacyclic Frobenius group of automorphisms},
  author={Evgenii I. Khukhro},
  year={2013}
}
Suppose that a finite group G admits a Frobenius group of automorphisms FH of coprime order with cyclic kernel F and complement H such that the fixed point subgroup CG(H) of the complement is nilpotent of class c. It is proved that G has a nilpotent characteristic subgroup of index bounded in terms of c, |CG(F )|, and |F | whose nilpotency class is bounded in terms of c and |H| only. This generalizes the previous theorem of the authors and P. Shumyatsky, where for the case of CG(F ) = 1 the… CONTINUE READING