直接有限阿贝尔群的一些遗传和超类

IF 0.6 3区数学 Q3 MATHEMATICS

Acta Mathematica Hungarica Pub Date : 2025-08-26 DOI:10.1007/s10474-025-01546-y

P. Danchev, B. Goldsmith, F. Karimi

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引用次数: 0

摘要

在对某些类阿贝尔群的遗传性质和超性质研究的基础上，我们深入探讨了由直接有限阿贝尔群组成的相当大的类的情况。试图将这些类联系起来，我们特别成功地证明了一个令人惊讶的准则：一个相对Hopfian群只有当它是扩展Bassian时才具有遗传Hopfian，以及一个相对Hopfian群只有当它是扩展Bassian时才具有超级Hopfian。在这方面，还证明了在稍微一般的情况下的其他有关的充分必要条件。

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On some hereditary and super classes of directly finite Abelian groups

Continuing recent studies of both the hereditary and super properties of certain classes of Abelian groups, we explore in-depth what is the situation in the quite large class consisting of directly finite Abelian groups.

Trying to connect some of these classes, we specifically succeeded to prove the surprising criteria that a relatively Hopfian group is hereditarily Hopfian only when it is extended Bassian, as well as that, a relatively Hopfian group is super Hopfian only when it is extended Bassian. In this aspect, additional relevant necessary and sufficient conditions in a slightly more general context are also proved.

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来源期刊

Acta Mathematica Hungarica 数学-数学

CiteScore

1.50

自引率

11.10%

发文量

审稿时长

4-8 weeks

期刊介绍： Acta Mathematica Hungarica is devoted to publishing research articles of top quality in all areas of pure and applied mathematics as well as in theoretical computer science. The journal is published yearly in three volumes (two issues per volume, in total 6 issues) in both print and electronic formats. Acta Mathematica Hungarica (formerly Acta Mathematica Academiae Scientiarum Hungaricae) was founded in 1950 by the Hungarian Academy of Sciences.