Geodesic
Abelian groups admitting fixed-point-free automorphisms of order $q^n$
Matematičeskie zametki, Tome 21 (1977) no. 2, pp. 239-250 
S. V. Larin. Abelian groups admitting fixed-point-free automorphisms of order $q^n$. Matematičeskie zametki, Tome 21 (1977) no. 2, pp. 239-250. http://geodesic.mathdoc.fr/item/MZM_1977_21_2_a12/
@article{MZM_1977_21_2_a12,
     author = {S. V. Larin},
     title = {Abelian groups admitting fixed-point-free automorphisms of order $q^n$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {239--250},
     year = {1977},
     volume = {21},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1977_21_2_a12/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

For a wide class of Abelian groups, necessary and sufficient conditions under which a group admits an automorphism of order $q^n$ are found; we also present necessary and sufficient conditions under which a group admits an automorphism $\varphi$ of order $q^n$ such that $\varphi^{qm}$ is a fixed-point-free automorphism for some $m.