{"title":"关于指数中心最多为 $$p^3$$ 的群的模态同构问题","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":null,"pages":null},"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":"{\"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\":null,\"pages\":null},\"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}","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}
引用次数: 0
摘要
让 p 是奇素数。我们证明，对于中心指数为\(p^3\)的有限 p 群，模态同构问题有一个肯定的答案，这与\(p = 2\) 的类似情况形成了强烈对比。
On the modular isomorphism problem for groups with center of index at most \(p^3\)
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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