Fitting classes and their associated injectors have been considered in a number of classes of locally finite groups [9, 8, 4, 5]. In particular, Dixon has considered the class [Lfr ] of countable locally finite groups with min −p for all primes p. He has shown that if the [Lfr ]-group G is radical (that is, it has an ascending locally nilpotent series) then G has locally nilpotent injectors, any two of which are isomorphic. Question 7.4.7 in [5] asks whether the restriction of being radical can be removed in this result.