My attention has been called to the fact that Theorem E1, quoted on p. 445 of my paper “On the embedding of a group in a join of given groups’, J. Austral. Math. Soc. 17 (1974), 434–495, is practically identical with Théoréme I (p. 47) of the second part of the three-part paper “Produit complet des groupes de permutations et probléme d'extension des groupes” by M. Krasner and L. Kaloujnine, Acta Sci. Math. Szeged 14 (1951), 39–66. My oversight in referring only to the third part of this important work, which contains the special case often quoted as the Kaloujnine-Krasner Theorem, is regrettable: it is the much more general and definitive Théoréme I which should be equally or better known by that name.