## Ian Hawthorn

*Nil series from arbitrary functions in group theory*

Comment.Math.Univ.Carolin. 59,1 (2018) 1-13.**Abstract:**In an earlier paper distributors were defined as a measure of how close an arbitrary function between groups is to being a homomorphism. Distributors generalize commutators, hence we can use them to try to generalize anything defined in terms of commutators. In this paper we use this to define a generalization of nilpotent groups and explore its basic properties.

**Keywords:** finite group; nilpotent; arbitrary functions; nil-series; distributor

**DOI:** DOI 10.14712/1213-7243.2015.240

**AMS Subject Classification:** 20D99

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