On the dual theory of a result of Bryce and Cossey

Abstract

In the theory of formations of finite soluble groups, a well known result of Bryce and Cossey is: a local formation F is a Fitting class if and only if every value of the canonical formation function F of F is a Fitting class. In this paper, we give the dual theory of the result of Bryce and Cossey. We proved that an ω-local (in particular, local) Fitting class F is a formation if and only if every value of the canonical ω-local (in particular, local) Hartley function F of F is a formation.