Frobenius groups with many involutions

Abstract

We consider a special class of Frobenius Groups, which generalizes the class of sharply 2-transitive groups in such a way that the construction of a neardomain can be generalized to the construction of a K-loop. The group then is shown to be a quasidirect product of that K-loop by a suitable automorphism group. The major advantage of this point of view is the existence of examples which are hoped to shed some light on the still open problem of the existence of proper neardomains.