Geodesic
Representations of the first degree of Abelian groups
Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 3, pp. 185-191.

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A complete description of $\operatorname{Hom}(G,\operatorname{Aut}V)$, where $V$ is a vector space of dimension $1$ on a finite field $\mathbb{F}_{q}$, on the rational field $\mathbb{Q}$, on the field of real numbers $\mathbb{R}$, and on the field of complex numbers $\mathbb{C}$ is given. The description is given in each of these four cases for any Abelian group $G$. 
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A. M. Sebel'din; A. L. Sylla. Representations of the first degree of Abelian groups. Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 3, pp. 185-191. http://geodesic.mathdoc.fr/item/FPM_2007_13_3_a17/

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