Geodesic
Vector groups with isomorphic holomorphs
Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 8, pp. 21-30.

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In this paper, vector groups whose holomorphs are isomorphic are studied. In connection with the studied problem, the concepts of a semi-characteristic and $\Gamma(G)$-decomposition of a group are introduced. The properties of such decompositions are described. Isomorphism conditions of holomorphically isomorphic vector groups are found. 
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I. E. Grinshpon. Vector groups with isomorphic holomorphs. Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 8, pp. 21-30. http://geodesic.mathdoc.fr/item/FPM_2012_17_8_a3/

[1] Bekker I. Kh., “O golomorfakh neredutsirovannykh abelevykh grupp”, Izv. vyssh. uchebn. zaved. Matematika, 1968, no. 8, 3–10 | MR | Zbl

[2] Bekker I. Kh., “O golomorfakh abelevykh grupp bez krucheniya”, Izv. vyssh. uchebn. zaved. Matematika, 1974, no. 3, 3–11 | MR | Zbl

[3] Bekker I. Kh., “Abelevy gruppy s izomorfnymi golomorfami”, Izv. vyssh. uchebn. zaved. Matematika, 1975, no. 3, 97–99 | MR | Zbl

[4] Bekker I. Kh., “Opredelyaemost redutsirovannykh abelevykh grupp bez krucheniya svoimi otnositelnymi golomorfami”, Abelevy gruppy i moduli, 1980, 3–19 | MR

[5] Bekker I. Kh., “Abelevy golomorfnye gruppy”, Mezhdunar. konf. Vsesibirskie chteniya po matematike i mekhanike, Izbrannye doklady, v. 1, Matematika, 1997, 43–47

[6] Grinshpon I. E., “Normalnye podgruppy golomorfov abelevykh grupp i pochti golomorfnyi izomorfizm”, Fundament. i prikl. mat., 13:3 (2007), 9–16 | MR | Zbl

[7] Kishkina Z. M., “Endomorfizmy $p$-primitivnykh abelevykh grupp bez krucheniya”, Izv. AN SSSR. Ser. mat., 9:3 (1945), 201–232 | MR | Zbl

[8] Mishina A. P., “O pryamykh slagaemykh polnykh pryamykh summ abelevykh grupp bez krucheniya ranga 1”, Sib. mat. zhurn., 3:2 (1962), 244–249 | Zbl

[9] Fuks L., Beskonechnye abelevy gruppy, v. 1, Mir, M., 1974

[10] Fuks L., Beskonechnye abelevy gruppy, v. 2, Mir, M., 1977

[11] Miller G. A., “On the multiple holomorph of a group”, Math. Ann., 66 (1908), 133–142 | DOI | MR

[12] Mills W. H., “On the non-isomorphism of certain holomorphs”, Trans. Am. Math. Soc., 74:3 (1953), 428–443 | DOI | MR | Zbl

[13] O'Neill J. D., “Direct summands of vector groups”, Acta Math. Acad. Sci. Hungar., 55:3–4 (1990), 207–209 | DOI | MR | Zbl

[14] Sasiada E., “On the isomorphism of decomposition of torsion-free Abelian groups into complete direct sum of group of rang one”, Bull. Acad. Polon. Sci., 7 (1959), 145–149 | MR | Zbl

[15] Sasiada E., “Proof that every countable and reduced torsion-free Abelian groups is slender”, Bull. Acad. Polon. Sci., 7 (1959), 143–144 | MR | Zbl