1. (1) N. Abel: [1] Untersuchung zweier unabhängig veränderlichen grössen x und y, wie f(x,y), welche die Eigenschaft haben, dass f(z,f(x,y)) eine symmetrische Funktion von z, x und y ist. Journal f. d. reiue u. angew. Math., Bd. 1 (1826). He investigated the functional equation (1) under the more restricted condition that f(x,f(y,z)) is a symmetric function of x, y and z, which, however, is superfluous, as it results from the fact that the continuous one parameter group is necessarily abelian.
2. (2) T. Hayashi: [1] On a functional equation treated by Abel. Zeitschr. f. Math. u. Phys., Vol. 44.
3. (2) T. Hayashi: [2] On a functional equation treated by Abel. Proc. Tokyo Math.-Phys. Soc., (1) Vol. 8.
4. (2) O. Sutô: [1] On some classes of functional equation. Tôhoku Math. Journ., Vol. 3 (1913).
5. (3) What we mean is identical with the parametric function f(x,y) introduced by Mineur with the following properties: 1º. For any numbers x, y and z, we have the relation (1). 2º. There exists a uniquely determined number e such that f(x,e)=x, f(e,x)=x. 3º. In the relation f(x,y)=z, a third member among x, y and z is uniquely determined if the other two are known, unless it touches with the relation 2º.