Abstract. The polynomial interpolation problem is considered for a class of subdirectly irreducible groups $G$ with abelian monolith $H$. The results give a possibility for a function $A\rightarrow H$ with $A$ a finite subset in $G$ to decide whether it is polynomial or not. In particular, this allows the determination of the number of the unary polynomial functions for certain finite groups.

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

Received July 6, 1994, and in revised form May 31, 1995. (Registered under 5676/2009.)