In order to describe sharply 2-transitive group, H.Karzel introduced the notion of a neardomain (F, +, ·). The difficulty of a neardomain is the additive structure (F, +) which need not be associative. A neardomain with an associative addition is already a nearfield. But till now no example of proper neardomain is known. We consider a special class of Frobenius groups –Frobenius groups with many involution- 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 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.