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Canonical and Algebraically Closed Groups in Universal Classes of Abelian Groups
Algebra and Logic ( IF 0.4 ) Pub Date : 2019-07-01 , DOI: 10.1007/s10469-019-09541-3 A. A. Mishchenko , V. N. Remeslennikov , A. V. Treier
Algebra and Logic ( IF 0.4 ) Pub Date : 2019-07-01 , DOI: 10.1007/s10469-019-09541-3 A. A. Mishchenko , V. N. Remeslennikov , A. V. Treier
Using sets of finitely generated Abelian groups closed under the discrimination operator, we describe principal universal classes 𝒦 within a quasivariety 𝔄p, the class of groups whose periodic part is a p-group for a prime p. Also the concept of an algebraically closed group in 𝒦 is introduced, and such groups are classified.
中文翻译:
阿贝尔群的泛类中的规范闭群和代数闭群
使用在判别算子下闭合的有限生成阿贝尔群的集合,我们描述了拟变异 𝔄p 中的主要泛类 𝒦,该类群的周期部分是质数 p 的 p 群。还引入了𝒦中代数闭群的概念,并对这些群进行了分类。
更新日期:2019-07-01
中文翻译:
阿贝尔群的泛类中的规范闭群和代数闭群
使用在判别算子下闭合的有限生成阿贝尔群的集合,我们描述了拟变异 𝔄p 中的主要泛类 𝒦,该类群的周期部分是质数 p 的 p 群。还引入了𝒦中代数闭群的概念,并对这些群进行了分类。