Abstract. We compute the unary polynomial functions on groups that arise as semidirect products of two groups $A, B$ with the property that every element of $B$ operates on $A$ by conjugation either trivially or as a fixed-point-free automorphism; in many cases, we obtain the number of polynomial functions on these groups.

AMS Subject Classification (1991): 08A40, 16Y30

Received November 17, 2000, and in revised form May 9, 2001. (Registered under 2828/2009.)