Equiangular tight frames and signature sets in groups

quiangular frames are an important class of finite dimensional frames because of their superior performance and numerous applications. The objective of this paper is to present a new tool to construct equiangular tight frames from groups. We prove that many equiangular tight frames arise from subsets of groups which we call signature sets. Subsequently, we define quasi-signature sets and examine real equiangular tight frames associated with these subsets of groups. This approach yields further results and establishes new correspondences. We extend these results to complex equiangular tight frames where the inner product between any pair of vectors is a common multiple of a cube root of unity and exhibit equiangular tight frames that arise from groups in this manner.