全射影阿贝尔的交换子自同态𝑝-groups

Pub Date : 2023-06-23 DOI:10.1515/jgth-2022-0197

P. Keef

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引用次数: 0

摘要

对于一个初等阿别群𝐺，Chekhlov和Danchev(2015)通过将人们的注意力限制在所有对易子自同态集合生成的𝐺自同态环的子群、子带和酉子带上，定义了Kaplansky的完全可及性概念的三个变体。他们提出了一个问题，即准确地描述哪些全射影群表现出这些形式的完全及物性。这个问题，以及一些密切相关的问题，都可以通过𝐺的Ulm函数得到完全的解答。

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Commutator endomorphisms of totally projective abelian 𝑝-groups

Abstract For a primary abelian group 𝐺, Chekhlov and Danchev (2015) defined three variations of Kaplansky’s notion of full transitivity by restricting one’s attention to the subgroup, the subring and the unitary subring of the endomorphism ring of 𝐺 generated by the collection of all commutator endomorphisms. They posed the problem of describing exactly which totally projective groups exhibit these forms of full transitivity. This problem, and some closely related questions, are completely answered using the Ulm function of 𝐺.

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