Nilpotent length of a finite solvable group with a frobenius group of automorphisms
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KünyeERCAN, G., GÜLOĞLU, İ.Ş., ÖĞÜT, E. (2014). Nilpotent length of a finite solvable group with a frobenius group of automorphisms. Communications in Algebra, 42 (11), pp. 4751-4756. http://dx.doi.org/10.1080/00927872.2013.823776.
We prove that a finite solvable group G admitting a Frobenius group FH of automorphisms of coprime order with kernel F and complement H such that [G, F] = G and C C G (F)(h) = 1 for all nonidentity elements h ∈ H, is of nilpotent length equal to the nilpotent length of the subgroup of fixed points of H.