Geodesic
On vanishing of the first cohomology groups over separable Abelian groups
Fundamentalʹnaâ i prikladnaâ matematika, Tome 8 (2002) no. 1, pp. 289-300 
E. V. Shaposhnikova. On vanishing of the first cohomology groups over separable Abelian groups. Fundamentalʹnaâ i prikladnaâ matematika, Tome 8 (2002) no. 1, pp. 289-300. http://geodesic.mathdoc.fr/item/FPM_2002_8_1_a21/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Conditions of vanishing of the first cohomology groups $\mathbb H^1(\Phi,G)$, where $G$ is a mixed separable Abelian group, $\Phi\leq\mathop{\mathrm{Aut}}G$, are obtained.

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[2] Bekker I. Kh., “Ob abelevykh gruppakh bez krucheniya s periodicheskimi gruppami avtomorfizmov”, Izv. vyssh. uchebn. zaved. Matem., 1986, no. 2, 3–12 | MR | Zbl

[3] Shaposhnikova E. V\@., O ravenstve nulyu pervykh grupp kogomologii nad smeshannymi separabelnymi abelevymi gruppami, Dep. v VINITI 12.03.97, No 748-V97

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[5] Maklein S., Gomologiya, Mir, M., 1966

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[8] Mills W. H., “The automorphisms of the holomorph of a finite Abelian group”, Trans. Amer. Math. Soc., 85:1 (1957), 1–34 | DOI | MR | Zbl

[9] Burbaki N., Elementy matematiki. Algebra, glava X. Gomologicheskaya algebra, Nauka, M., 1987 | MR