Criteria for wild nearfields (Q311049)

Nearfields are generalizations of skew fields: only one of the two distributive laws is required to hold. Dickson nearfields are constructed from skew fields by modifying the multiplication using skew field automorphisms. The author provides sufficient criteria for a nearfield (of dimension \(2\) over its kernel) to be wild, i.e. not a Dickson nearfield.NEWLINENEWLINENecessarily these criteria are rather technical. The first criterion shows that certain nearfields of characteristic \(3\) constructed in [\textit{T. Grundhöfer} and \textit{M. Grüninger}, J. Geom. 107, No. 2, 317--328 (2016; Zbl 1369.12007), Theorem 3.2], are wild. A second criterion implies that all nearfields in [loc. cit., Theorem 3.1], also those with characteristic \(2\), are wild.