The Fitting length of a finite soluble group and the number of conjugacy classes of its maximal nilpotent subgroups

Abstract

It is shown that there exists a logarithmic upper bound on the Fitting length h ( G ) of a finite soluble group G in terms of the number ν( G ) of the conjugacy classes of its maximal nilpotent subgroups. For ν( G ) = 3, the best possible bound on h ( G ) is shown to be 4.