{"title":"Separability properties of nilpotent ℚ[𝑥]-powered groups II","authors":"Stephen Majewicz, Marcos Zyman","doi":"10.1515/jgth-2023-0288","DOIUrl":null,"url":null,"abstract":"In this paper, we study nilpotent <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>-powered groups that satisfy the following property: for some set of primes 𝜔 in <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>, 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":50188,"journal":{"name":"Journal of Group Theory","volume":"8 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Group Theory","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/jgth-2023-0288","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
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.
期刊介绍：
The Journal of Group Theory is devoted to the publication of original research articles in all aspects of group theory. Articles concerning applications of group theory and articles from research areas which have a significant impact on group theory will also be considered.
Topics:
Group Theory-
Representation Theory of Groups-
Computational Aspects of Group Theory-
Combinatorics and Graph Theory-
Algebra and Number Theory
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