On elementary domains of partial projective representations of groups

Abstract

We characterize the finite groups containing only elementary domains of factor sets of  partial projective representations. A condition for a finite subset  \(A\) of a group \(G,\) which contains the unity of the group, to induce an elementary partial representation, of \(G\) whose (idempotent) factor set is total is given. Finally, we characterize  the elementary partial representation of abelian groups of degrees \(\le 4\) with total factor set.