零势ℚ[𝑥]幂群的可分性特性 II

Pub Date : 2024-08-05 DOI:10.1515/jgth-2023-0288
Stephen Majewicz, Marcos Zyman
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stretchy=\"false\">]</m:mo> </m:mrow> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_jgth-2023-0288_ineq_0001.png\"/> <jats:tex-math>\\mathbb{Q}[x]</jats:tex-math> </jats:alternatives> </jats:inline-formula>, every <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mi>ω</m:mi> <m:mo>′</m:mo> </m:msup> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_jgth-2023-0288_ineq_0003.png\"/> <jats:tex-math>\\omega^{\\prime}</jats:tex-math> </jats:alternatives> </jats:inline-formula>-isolated <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi mathvariant=\"double-struck\">Q</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=\"false\">[</m:mo> <m:mi>x</m:mi> <m:mo stretchy=\"false\">]</m:mo> </m:mrow> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_jgth-2023-0288_ineq_0001.png\"/> <jats:tex-math>\\mathbb{Q}[x]</jats:tex-math> </jats:alternatives> </jats:inline-formula>-subgroup in some family of its <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi mathvariant=\"double-struck\">Q</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=\"false\">[</m:mo> <m:mi>x</m:mi> <m:mo stretchy=\"false\">]</m:mo> </m:mrow> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_jgth-2023-0288_ineq_0001.png\"/> <jats:tex-math>\\mathbb{Q}[x]</jats:tex-math> </jats:alternatives> </jats:inline-formula>-subgroups is finite 𝜔-type separable.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-05","publicationTypes":"Journal 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引用次数: 0

摘要

本文研究满足以下性质的无幂 Q [ x ] \mathbb{Q}[x] 有幂群：对于 Q [ x ] \mathbb{Q}[x]中的某个prime 細集，其 Q [ x ] \mathbb{Q}[x]-子群的某个族中的每Ω ′ \omega^{\prime} -隔离的 Q [ x ] \mathbb{Q}[x]-子群都是有限娀型可分离的。
本文章由计算机程序翻译，如有差异，请以英文原文为准。
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Separability properties of nilpotent ℚ[𝑥]-powered groups II
In this paper, we study nilpotent Q ⁢ [ x ] \mathbb{Q}[x] -powered groups that satisfy the following property: for some set of primes 𝜔 in Q ⁢ [ x ] \mathbb{Q}[x] , every ω ′ \omega^{\prime} -isolated Q ⁢ [ x ] \mathbb{Q}[x] -subgroup in some family of its Q ⁢ [ x ] \mathbb{Q}[x] -subgroups is finite 𝜔-type separable.
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