Abstract:In this paper we consider finite loops and discuss the problem which nilpotent groups are isomorphic to the inner mapping group of a loop. We recall some earlier results and by using connected transversals we transform the problem into a group theoretical one. We will get some new answers as we show that a nilpotent group having either C_{p^k} \times C_{p^l}, k > l \geq 0 as the Sylow p-subgroup for some odd prime p or the group of quaternions as the Sylow 2-subgroup may not be loop capable.
Keywords: loop, group, connected transversals
AMS Subject Classification: 20D10 20N05