**MARIO SERVI**
*Equazioni caratteristiche per la commutatività
*

**Pages** 171-177

**Received:** 15 July 1993

**AMS Classification :** 03B99

**Abstract**
Let f be a binary operation on the positive integers obtained by primitive recursion from g and φ ; in a preceeding work
( see [**3**] we gave a sufficient condition on g and φ for f to be commutative. Here, after disproving the necessity of that condition, we give a set of
equations of the defining functions whose satisfaction is both necessary and sufficient for the commutativity of
the function to be defined.