Geodesic
On elementary domains of partial projective representations of groups
Algebra and discrete mathematics, Tome 15 (2013) no. 1, pp. 63-82.

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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.
Keywords: elementary partial representation, partial projective representation, elementary domain, total factor set. 
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H. Pinedo. On elementary domains of partial projective representations of groups. Algebra and discrete mathematics, Tome 15 (2013) no. 1, pp. 63-82. http://geodesic.mathdoc.fr/item/ADM_2013_15_1_a6/

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