Derived p-Length of a p-Soluble Group with Bounded Indices of Fitting p-Subgroups in Their Normal Closures

Abstract

Let G be a p-soluble group. Then G has a subnormal series whose factors are either p′-groups or Abelian p-groups. The smallest number of Abelian p-factors in all subnormal series of G of this kind is called the derived p-length of G. A subgroup H of the group G is called a Fitting subgroup if H ≤ F(G). The existence of a functional dependence of the estimate of derived p-length of a p-soluble group on the value of indices of the Fitting p-subgroups in their normal closures is established.