Geodesic
Exact projective representations of Abelian groups
Matematičeskie zametki, Tome 10 (1971) no. 3, pp. 345-354.

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A complete description of the finite Abelian groups having exact irreducible projective representations over a field $F$ comprising a finite extension of the rational number field or rational $p$-adic number field is presented. 
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     author = {L. F. Barannik},
     title = {Exact projective representations of {Abelian} groups},
     journal = {Matemati\v{c}eskie zametki},
     pages = {345--354},
     publisher = {mathdoc},
     volume = {10},
     number = {3},
     year = {1971},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1971_10_3_a12/}
}
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L. F. Barannik. Exact projective representations of Abelian groups. Matematičeskie zametki, Tome 10 (1971) no. 3, pp. 345-354. http://geodesic.mathdoc.fr/item/MZM_1971_10_3_a12/