On Weakly Transitive Torsion-Free Abelian Groups
Copyright policy )On Weakly Transitive Torsion-Free Abelian Groups
This short note adds new information on a previous paper with the same subject by \textit{B. Goldsmith} and \textit{L. Strüngmann} [Commun. Algebra 33, No. 4, 1177--1191 (2005; Zbl 1142.20032)]. The results are: Proposition 2. If \(A\) is a reduced torsion-free group with strongly indecomposable pure subgroups and the set \(T(A)\) of types of all its nonzero elements satisfies the maximality condition, then \(A\) is weakly transitive. Theorem. If \(A\) is a quasi-homogeneous torsion-free rank 2 group, then \(A\) is weakly transitive if and only if \(A\) satisfies one of the following conditions: (1) \(A\) is a strongly indecomposable group; (2) \(A\) is a homogeneous completely decomposable group; (3) \(A=B\oplus G\), where \(t(G)>t(B)\) and the group \(G\) satisfies condition (ii) of Theorem 6; (4) the endomorphism ring \(E(A)\) of the group \(A\) is commutative.
- Tomsk State Pedagogical University Russian Federation
- National Research University of Electronic Technology Russian Federation
strongly indecomposable group, слабо транзитивные абелевы группы без кручения, Torsion-free groups, finite rank, квазиоднородные группы без кручения, Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups, torsion-free abelian group, слабо транзитивный эндоморфизм, чистые подгруппы, мономорфизм, слабо транзитивные группы, weakly transitive
strongly indecomposable group, слабо транзитивные абелевы группы без кручения, Torsion-free groups, finite rank, квазиоднородные группы без кручения, Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups, torsion-free abelian group, слабо транзитивный эндоморфизм, чистые подгруппы, мономорфизм, слабо транзитивные группы, weakly transitive
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