Abstract. In the present paper we give an algorithm to compute generators of power integral bases having ``small" coordinates in an integral basis in sextic fields containing a cubic subfield. As an application of the method, we give a sufficient condition for infinite parametric families of number fields of this type to have power integral basis. To illustrate the statement we construct parametric families of fields and describe generators of power integral bases in them.

AMS Subject Classification (1991): 11Y50; 11D57

Received June 6, 2001, and in revised form October 17, 2001. (Registered under 2880/2009.)