A fitting class construction

Summary We present a Fitting Class construction which exploits the properties of a certain class of finite soluble groups of nilpotent length three, called-groups in the paper. In addition we look at a wider class of groups, called in the paper, also of nilpotent length three and examine the question as to what-groups are in.A number of examples are given to illuminate the various classes.The author would like to thank HermannHeineken for supervising his dissertation, from which this paper has sprung, the German Academic Exchange Service (DAAD) for enabling him to study with Prof. Heineken at Universität Würzburg and An Roinn Oideachais for the fellowship which is at present supporting him at University College, Galway.