On a relation between injectors and certain complemented chief factors of finite soluble groups

Abstract

The Fitting class of finite soluble π-groups, where π is an arbitrary set of primes, has the property that each complement of an -avoided, complemented chief factor of any finite soluble group G contains an -injector of G. In other words, each -avoided, complemented chief factor of G is -complemented in the sense of Hartley (see [2]).