Geodesic
Determinateness of torsion-free Abelian groups by their holomorphs and almost holomorphic isomorphism
Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 8, pp. 35-46 
S. Ya. Grinshpon; I. E. Grinshpon. Determinateness of torsion-free Abelian groups by their holomorphs and almost holomorphic isomorphism. Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 8, pp. 35-46. http://geodesic.mathdoc.fr/item/FPM_2012_17_8_a5/
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     title = {Determinateness of torsion-free {Abelian} groups by their holomorphs and almost holomorphic isomorphism},
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we study holomorphically isomorphic Abelian groups, i.e., Abelian groups with isomorphic holomorphs. We also study a generalization of the concept of holomorphic isomorphism, namely, almost holomorphic isomorphism, which is deeply connected with normal Abelian subgroups of holomorphs of Abelian groups. Torsion-free Abelian groups that are determined by their holomorphs are highlighted from different classes. In particular, it has been found that any homogeneous separable group can be determined by its holomorph in the class of all Abelian groups.

[1] Bekker I. Kh., “O golomorfakh abelevykh grupp”, Sib. mat. zhurn., 5:6 (1964), 1228–1238 | MR | Zbl

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

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

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

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

[6] Bekker I. Kh., Grinshpon S. Ya., “Pochti golomorfno izomorfnye primarnye abelevy gruppy”, Gruppy i moduli, Mezhvuz. temat. sb. nauch. tr., 1976, 90–103

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

[8] Grinshpon S. Ya., “Pochti golomorfno izomorfnye abelevy gruppy”, Tr. TGU. Voprosy matematiki, 220:3 (1975), 78–84

[9] Grinshpon S. Ya., “O stroenii vpolne kharakteristicheskikh podgrupp abelevykh grupp bez krucheniya”, Abelevy gruppy i moduli, Tomsk, 1982, 56–92 | MR

[10] Grinshpon S. Ya., “Vpolne kharakteristicheskie podgruppy abelevykh grupp i vpolne tranzitivnost”, Fundament. i prikl. mat., 8:2 (2002), 407–473 | MR | Zbl

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

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

[13] Mills W. H., “Multiple holomorphs of finitely generated Abelian groups”, Trans. Am. Math. Soc., 71:3 (1950), 379–392 | DOI | MR

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