P-GROUPS IN THE BETTI-MATHIEU GROUP

We construct a Sylow p-subgroup of the Betti-Mathieu group by characte rizing a certain type of polynomial through the use of the trace funct ion and a normal basis over a finite field. It follows from this that a complete lattice of normal subgroups of the Sylow p-subgroup under i nclusion will be determined together with an explicit polynomial repre sentation of the normal subgroups.