Abstract
Given any translation planeU, one can define the nucleusN as the subset of trace-preserving mappings of the point set satisfying a special linearity condition.N is always a nearfield isomorphic to the right-nucleus of a coordinatizing (left-)quasifield. If the transitivity axiom (NT) is valid,N is planar and the plane is isomorphic to the nearfield plane overN. Finally it is shown that (NT) is equivalent to the usual (P, OQ)-transitivity condition for nearfield planes.
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