Geodesic
About determinableness of an Abelian group by its holomorph in the class of all Abelian groups
Fundamentalʹnaâ i prikladnaâ matematika, Tome 8 (2002) no. 1, pp. 17-25
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For an Abelian group without elements of order 2 the following results were obtained: 1) a criterion for its determinableness by its holomorph in the class of all Abelian groups; 2) a criterion for its characteristicness in its holomorph. 
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I. Kh. Bekker; V. N. Nedov. About determinableness of an Abelian group by its holomorph in the class of all Abelian groups. Fundamentalʹnaâ i prikladnaâ matematika, Tome 8 (2002) no. 1, pp. 17-25. http://geodesic.mathdoc.fr/item/FPM_2002_8_1_a1/

[1] Mills W. H., “Multiple holomorphs of finitely generated abelian groups”, Trans. Amer. Math. Soc., 74:3 (1953), 428–443 | DOI | MR | Zbl

[2] Bekker I. Kh., Kozhukhov S. F., Avtomorfizmy abelevykh grupp bez krucheniya, Izd-vo Tomskogo un-ta, Tomsk, 1988 | Zbl

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[5] Fuks L., Beskonechnye abelevy gruppy, T. 2, Mir, M., 1977