Geodesic
Sequences of Endomorphism Groups of Abelian Groups
Matematičeskie zametki, Tome 104 (2018) no. 2, pp. 309-317

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

In the paper, Problem 18.3 of the book “Abelian groups” (2015) by L. Fuchs is solved in the case of Abelian groups with finite $p$-ranks. For an Abelian group $A$, a sequence of groups $(A_n)$ is considered, where $A_0=A$ and $A_{n+1}=\operatorname{End}A_n$. It is shown that, if all $p$-ranks of the group $A$ are finite, then this sequence can stabilize either after $A_0$ or after $A_1$.
Keywords: Abelian group, $E$-ring, $E$-group, $p$-rank. 
@article{MZM_2018_104_2_a13,
     author = {E. A. Timoshenko and A. V. Tsarev},
     title = {Sequences of {Endomorphism} {Groups} of {Abelian} {Groups}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {309--317},
     publisher = {mathdoc},
     volume = {104},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_104_2_a13/}
}
TY  - JOUR
AU  - E. A. Timoshenko
AU  - A. V. Tsarev
TI  - Sequences of Endomorphism Groups of Abelian Groups
JO  - Matematičeskie zametki
PY  - 2018
SP  - 309
EP  - 317
VL  - 104
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2018_104_2_a13/
LA  - ru
ID  - MZM_2018_104_2_a13
ER  - 
%0 Journal Article
%A E. A. Timoshenko
%A A. V. Tsarev
%T Sequences of Endomorphism Groups of Abelian Groups
%J Matematičeskie zametki
%D 2018
%P 309-317
%V 104
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2018_104_2_a13/
%G ru
%F MZM_2018_104_2_a13
E. A. Timoshenko; A. V. Tsarev. Sequences of Endomorphism Groups of Abelian Groups. Matematičeskie zametki, Tome 104 (2018) no. 2, pp. 309-317. http://geodesic.mathdoc.fr/item/MZM_2018_104_2_a13/