Geodesic
On determinability of a completely decomposable torsion-free Abelian group by its automorphism group
Fundamentalʹnaâ i prikladnaâ matematika, Tome 20 (2015) no. 5, pp. 31-37
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper, we consider the question of determinability of an Abelian group by its automorphism group in the class of completely decomposable torsion-free Abelian groups whose direct summands of rank $1$ have idempotent types. 
@article{FPM_2015_20_5_a3,
     author = {V. K. Vildanov},
     title = {On determinability of a~completely decomposable torsion-free {Abelian} group by its automorphism group},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {31--37},
     year = {2015},
     volume = {20},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2015_20_5_a3/}
}
TY  - JOUR
AU  - V. K. Vildanov
TI  - On determinability of a completely decomposable torsion-free Abelian group by its automorphism group
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2015
SP  - 31
EP  - 37
VL  - 20
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/FPM_2015_20_5_a3/
LA  - ru
ID  - FPM_2015_20_5_a3
ER  - 
%0 Journal Article
%A V. K. Vildanov
%T On determinability of a completely decomposable torsion-free Abelian group by its automorphism group
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2015
%P 31-37
%V 20
%N 5
%U http://geodesic.mathdoc.fr/item/FPM_2015_20_5_a3/
%G ru
%F FPM_2015_20_5_a3
V. K. Vildanov. On determinability of a completely decomposable torsion-free Abelian group by its automorphism group. Fundamentalʹnaâ i prikladnaâ matematika, Tome 20 (2015) no. 5, pp. 31-37. http://geodesic.mathdoc.fr/item/FPM_2015_20_5_a3/

[1] Vildanov V. K., “Opredelyaemost vpolne razlozhimoi abelevoi gruppy ranga $2$ svoei gruppoi avtomorfizmov”, Vestn. Nizhegorodsk. un-ta im. N. I. Lobachevskogo, 2011, no. 3(1), 174–177

[2] Vildanov V. K., “Opredelyaemost vpolne razlozhimoi blochno zhestkoi abelevoi gruppy bez krucheniya ee gruppoi avtomorfizmov”, Fundament. i prikl. matem., 17:8 (2011/2012), 13–19 | MR

[3] Sebeldin A. M., “Polnye pryamye summy abelevykh grupp bez krucheniya ranga $1$ s izomorfnymi gruppami ili koltsami endomorfizmov. I”, Matem. zametki, 14:6 (1973), 867–878 | MR

[4] Fuks L., Beskonechnye abelevy gruppy, v. 1, Mir, M., 1974; v. 2, 1977

[5] Leptin H., “Abelsche $p$-gruppen und ihre Automorphismengruppen”, Math. Z., 73 (1960), 235–253 | DOI | MR | Zbl

[6] Liebert W., “Isomorphic automorphism groups of primary Abelian groups”, Abelian Group Theory, Proc. of the 1985 Oberwolfach Conf., Gordon and Breach, New York, 1987, 9–31 | MR