Fitting height of groups and of fixed points

Nilpotent Length of a Finite Solvable Group with a Frobenius Group of Automorphisms

“…We proceed by induction on the order of G. As G = [G, F ] and (|G| , |F H|) = 1, there exists an irreducible F H-towerP 1 , ...,P n in the sense of [3] where…”

On finite groups in which coprime commutators are covered by few cyclic subgroups

“…Turull introduced in [12] the concept of an irreducible B-tower and showed that a soluble group G has Fitting height h if and only if h is maximal such that there exists an irreducible tower of height h consisting of subgroups of G (see Lemmas 1.4 and 1.9(3) in [12]). We will now remind the reader some of the properties of subgroups forming an irreducible tower (we require only the case B = 1 and refer to these objects simply as "towers").…”

On the Fitting height of a finite group

“…Turull introduced in [7] the concept of a B-tower. We will require only few properties of these subgroups in the particular case that B ¼ 1.…”