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Article

Hawthorn, Ian
Nil series from arbitrary functions in group theory. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 59 (2018), issue 1, pp. 1-13
MSC: 20D99 | MR 3783804 | Zbl 06890392 | DOI: 10.14712/1213-7243.2015.240
Keywords:
finite group; nilpotent; arbitrary functions; nil-series; distributor
Summary:
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.
References:
[1] Dembowski P.: Finite Geometries. Springer, Berlin, 1968. Zbl 0865.51004
[2] Hawthorn I., Guo Y.: Arbitrary functions in group theory. New Zealand J. Math. 45 (2015), 1–9.
[3] Pott A.: Finite Geometry and Character Theory. Springer, Berlin, 1995.
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