On some properties of endomorphism rings of Abelian groups
Fundamentalʹnaâ i prikladnaâ matematika, Tome 20 (2015) no. 5, pp. 131-139.

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Some equivalent conditions under which a group can be (fully) transitive, endotransitive, or weakly transitive are presented.
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V. M. Misyakov. On some properties of endomorphism rings of Abelian groups. Fundamentalʹnaâ i prikladnaâ matematika, Tome 20 (2015) no. 5, pp. 131-139. http://geodesic.mathdoc.fr/item/FPM_2015_20_5_a12/

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

[2] Grinshpon S. Ya., “Vpolne kharakteristicheskie podgruppy abelevykh grupp i vpolne tranzitivnost”, Fundament. i prikl. matem., 8:2 (2002), 407–472 | MR

[3] Grinshpon S. Ya., Misyakov V. M., “O vpolne tranzitivnykh abelevykh gruppakh”, Abelevy gruppy i moduli, 1986, 12–27

[4] Grinshpon S. Ya., Misyakov V. M., “Vpolne tranzitivnost pryamykh proizvedenii abelevykh grupp”, Abelevy gruppy i moduli, 1991, 23–30 | MR

[5] Dobrusin Yu. B., “O prodolzheniyakh chastichnykh endomorfizmov abelevykh grupp bez krucheniya. II”, Abelevy gruppy i moduli, 5, 1985, 31–41

[6] Dobrusin Yu. B., “O prodolzheniyakh chastichnykh endomorfizmov abelevykh grupp bez krucheniya”, Abelevy gruppy i moduli, 4, 1986, 36–53

[7] Krylov P. A., “O vpolne kharakteristicheskikh podgruppakh abelevykh grupp bez krucheniya”, Sbornik aspirantskikh rabot po matematike, Izd-vo Tomsk. un-ta, Tomsk, 1973, 15–20

[8] Krylov P. A., “Nekotorye primery kvaziservantno in'ektivnykh i tranzitivnykh abelevykh grupp bez krucheniya”, Abelevy gruppy i moduli, 1988, 81–99 | MR | Zbl

[9] Krylov P. A., “Vpolne tranzitivnye abelevy gruppy bez krucheniya”, Algebra i logika, 29:5 (1990), 549–560 | MR | Zbl

[10] Krylov P. A., Mikhalev A. V., Tuganbaev A. A., Svyazi abelevykh grupp i ikh kolets endomorfizmov, TGU, Tomsk, 2002

[11] Misyakov V. M., “Vpolne tranzitivnost redutsirovannykh abelevykh grupp”, Abelevy gruppy i moduli, 1994, 134–156 | MR | Zbl

[12] Fuks L., Beskonechnye abelevy gruppy, v. I, Mir, M., 1974

[13] Fuks L., Beskonechnye abelevy gruppy, v. II, Mir, M., 1977

[14] Chekhlov A. R., “Vpolne tranzitivnye gruppy bez krucheniya konechnogo $p$-ranga”, Algebra i logika, 40:6 (2001), 698–715 | MR | Zbl

[15] Chekhlov A. R., “Ob odnom klasse endotranzitivnykh grupp”, Matem. zametki, 69:6 (2001), 944–949 | DOI | MR | Zbl

[16] Carroll D., Goldsmith B., “On transitive and fully transitive Abelian $p$-groups”, Proc. Royal Irish Academy, 96A:1 (1996), 33–41 | MR | Zbl

[17] Corner A. L. S., “The independence of Kaplansly's notions of transitivity and full transitivity”, Quart. J. Math. Oxford, 27:105 (1976), 15–20 | DOI | MR | Zbl

[18] Danchev P. V., Goldsmith B., “On socle-regularity and some notions of transitivity for Abelian $p$-groups”, J. Commut. Algebra, 3:3 (2011), 301–319 | DOI | MR | Zbl

[19] Dugas M., Shelah S., “$E$-transitive groups in $L$”, Abelian Group Theory (Perth, 1987), Contemp. Math., 87, Amer. Math. Soc., Providence, 1989, 191–199 | DOI | MR

[20] Files S., “On transitive mixed Abelian groups”, Abelian Group Theory, Proc. of the Int. Conf. at Colorado Springs, Lect. Notes Pure Appl. Math., 182, Marcel Dekker, New York, 1996, 243–251 | MR | Zbl

[21] Files S., “Transitivity and full transitivity for nontorsion modules”, J. Algebra, 197 (1997), 468–478 | DOI | MR | Zbl

[22] Files S., Goldsmith B., “Transitive and fully transitive groups”, Proc. Amer. Math. Soc., 126:6 (1998), 1605–1610 | DOI | MR | Zbl

[23] Goldsmith B., Strungmann L., “Torsion-free weakly transitive Abelian groups”, Commun. Algebra, 33 (2005), 1177–1191 | DOI | MR | Zbl

[24] Goldsmith B., Strungmann L., “Some transitivity results for torsion Abelian groups”, Houston J. Math., 33:4 (2007), 941–957 | MR | Zbl

[25] Griffith P., “Transitive and fully transitive primary Abelian groups”, Pacific J. Math., 25:2 (1968), 249–254 | DOI | MR | Zbl

[26] Hausen J., “E-transitive torsion-free Abelian groups”, J. Algebra, 107 (1987), 17–27 | DOI | MR | Zbl

[27] Hennecke G., Strüngmann L., “Transitivity and full transitivity for $p$-local modules”, Arch. Math., 74 (2000), 321–329 | DOI | MR | Zbl

[28] Hill P., “On transitive and fully transitive primary groups”, Proc. Amer. Math. Soc., 22:2 (1969), 414–417 | DOI | MR | Zbl

[29] Kaplansky I., Infinite Abelian Groups, Univ. of Michigan Press, Ann Arbor, 1954 | MR | Zbl

[30] Meehan C., Strungmann L., “Rational rings related to weakly transitive torsion-free groups”, J. Algebra Its Appl., 8:5 (2009), 723–732 | DOI | MR | Zbl

[31] Paras A., Strungmann L., “Fully transitive $p$-groups with finite first Ulm subgroup”, Proc. Amer. Math. Soc., 131 (2003), 371–377 | DOI | MR | Zbl