Number of terms in the group determinant

Abstract

In this paper, we prove that when the number of terms in the group determinant of order odd prime p is divided by p, the remainder is 1. In addition, we give a table of the number of terms in kth power of the group determinant of the cyclic group of order n for n≤10and k≤6, and also give a table of one for every group of order at most 15. These tables raise some questions for us about the number of terms in the group determinants.

Keywords

• Group determinant
• Monomial symmetric polynomial
• Cyclic group