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 $k$th power of the group determinant of the cyclic group of order $n$ for $n\le 10$ and $k\le 6$, 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.