Multiplication Groups of Finite Loops That Fix at Most Two Points,

For a loop Q(•, 1) define its multiplication group by Mlt Q = La, Ra; a Q , where La : x ax and Ra : x xa. Suppose that Q is not an abelian group and that every non-identical permutation contained in Mlt Q fixes at most two elements. We show that if Q is finite, then there exists no such loop.