{"title":"On the modular isomorphism problem for groups with center of index at most \\(p^3\\)","authors":"Sofia Brenner, Diego García-Lucas","doi":"10.1007/s00013-024-01977-z","DOIUrl":null,"url":null,"abstract":"<div><p>Let <i>p</i> be an odd prime number. We show that the modular isomorphism problem has a positive answer for finite <i>p</i>-groups whose center has index <span>\\(p^3\\)</span>, which is a strong contrast to the analogous situation for <span>\\(p = 2\\)</span>.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"122 5","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-024-01977-z.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Archiv der Mathematik","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00013-024-01977-z","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
Let p be an odd prime number. We show that the modular isomorphism problem has a positive answer for finite p-groups whose center has index \(p^3\), which is a strong contrast to the analogous situation for \(p = 2\).
期刊介绍：
Archiv der Mathematik (AdM) publishes short high quality research papers in every area of mathematics which are not overly technical in nature and addressed to a broad readership.
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