p-groups in the Betti-Mathieu group Original Research Article

We construct a Sylow p-subgroup of the Betti-Mathieu group by characterizing a certain type of polynomial through the use of the trace function 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 inclusion will be determined together with an explicit polynomial representation of the normal subgroups.