This article is cited in 3 papers

Sequences of Endomorphism Groups of Abelian Groups

E. A. Timoshenko^a, A. V. Tsarev<sup>b

a</sup> Tomsk State University
^b Moscow State Pedagogical University

Abstract: 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.

UDC: 512.541

Received: 01.06.2017

DOI: 10.4213/mzm11711

 English version: Mathematical Notes, 2018, 104:2, 309–315

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