Multiplication groups of finite loops that fix at most two points
Let \(Q\) be a finite loop (quasigroup with identity), \(L_a(x):=ax\), \(R_a(x):=xa\). A proof is offered that \(Q\) has to be an Abelian group if every permutation of its multiplication group \(\{L_a,R_a\mid a\in Q\}\) has at most two fixed points. An extension to the infinite case is alluded to in the introduction.
scientific article; zbMATH DE number 1563177