Definability of Abelian Groups by Homomorphism Groups and Endomorphism Semigroups
Matematičeskie zametki, Tome 84 (2008) no. 4, pp. 595-601.

Voir la notice de l'article provenant de la source Math-Net.Ru

In the paper, the isomorphism problem for completely decomposable Abelian torsion-free groups of finite rank is treated under the assumption that the groups of homomorphisms of these groups into some Abelian group are isomorphic and, moreover, the endomorphism semigroups of the groups are isomorphic.
Keywords: completely decomposable Abelian group, endomorphism semigroup, almost divisible group.
Mots-clés : torsion-free group
@article{MZM_2008_84_4_a10,
     author = {A. M. Sebel'din and A. E. Smorkalova},
     title = {Definability of {Abelian} {Groups} by {Homomorphism} {Groups} and {Endomorphism} {Semigroups}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {595--601},
     publisher = {mathdoc},
     volume = {84},
     number = {4},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2008_84_4_a10/}
}
TY  - JOUR
AU  - A. M. Sebel'din
AU  - A. E. Smorkalova
TI  - Definability of Abelian Groups by Homomorphism Groups and Endomorphism Semigroups
JO  - Matematičeskie zametki
PY  - 2008
SP  - 595
EP  - 601
VL  - 84
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2008_84_4_a10/
LA  - ru
ID  - MZM_2008_84_4_a10
ER  - 
%0 Journal Article
%A A. M. Sebel'din
%A A. E. Smorkalova
%T Definability of Abelian Groups by Homomorphism Groups and Endomorphism Semigroups
%J Matematičeskie zametki
%D 2008
%P 595-601
%V 84
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2008_84_4_a10/
%G ru
%F MZM_2008_84_4_a10
A. M. Sebel'din; A. E. Smorkalova. Definability of Abelian Groups by Homomorphism Groups and Endomorphism Semigroups. Matematičeskie zametki, Tome 84 (2008) no. 4, pp. 595-601. http://geodesic.mathdoc.fr/item/MZM_2008_84_4_a10/

[1] L. Fuks, Beskonechnye abelevy gruppy, t. 1, Mir, M., 1974 | MR | Zbl

[2] A. M. Sebeldin, “O gruppakh gomomorfizmov abelevykh grupp bez krucheniya”, Gruppy i moduli, Izd-vo Tomskogo gos. un-ta, Tomsk, 1976, 70–77

[3] A. M. Sebeldin, A. E. Smorkalova, “Opredelyaemost gruppami gomomorfizmov sprava v klasse vpolne razlozhimykh abelevykh grupp bez krucheniya”, Algebra i lineinaya optimizatsiya, Trudy mezhdunarodnogo seminara, posvyaschennogo 90-letiyu so dnya rozhdeniya S. N. Chernikova (3–5 iyunya 2002 g.), Izd-vo UrO RAN, Ekaterinburg, 2002, 187–192 | MR

[4] A. M. Sebeldin, “Usloviya izomorfizma vpolne razlozhimykh abelevykh grupp bez krucheniya s izomorfnymi koltsami endomorfizmov”, Matem. zametki, 11:4 (1972), 403–408 | MR | Zbl

[5] A. M. Sebeldin, “Opredelyaemost separabelnykh abelevykh grupp bez krucheniya polugruppami endomorfizmov”, Algebra i logika, 34:5 (1995), 523–530 | MR | Zbl