{"title":"A note on \n \n fsg\n $\\text{fsg}$\n groups in p-adically closed fields","authors":"Will Johnson","doi":"10.1002/malq.202200026","DOIUrl":null,"url":null,"abstract":"<p>Let <i>G</i> be a definable group in a <i>p</i>-adically closed field <i>M</i>. We show that <i>G</i> has finitely satisfiable generics (<math>\n <semantics>\n <mtext>fsg</mtext>\n <annotation>$\\text{fsg}$</annotation>\n </semantics></math>) if and only if <i>G</i> is definably compact. The case <math>\n <semantics>\n <mrow>\n <mi>M</mi>\n <mo>=</mo>\n <msub>\n <mi>Q</mi>\n <mi>p</mi>\n </msub>\n </mrow>\n <annotation>$M = \\mathbb {Q}_p$</annotation>\n </semantics></math> was previously proved by Onshuus and Pillay.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/malq.202200026","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Let G be a definable group in a p-adically closed field M. We show that G has finitely satisfiable generics () if and only if G is definably compact. The case was previously proved by Onshuus and Pillay.
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