{"title":"砖块的克利福德定理","authors":"Yuta Kozakai , Arashi Sakai","doi":"10.1016/j.jalgebra.2024.09.021","DOIUrl":null,"url":null,"abstract":"<div><div>Let <em>G</em> be a finite group, <em>N</em> a normal subgroup of <em>G</em>, and <em>k</em> a field of characteristic <span><math><mi>p</mi><mo>></mo><mn>0</mn></math></span>. In this paper, we formulate the brick version of Clifford's theorem under suitable assumptions and prove it by using the theory of wide subcategories. As an application of our theorem, we consider the restrictions of semibricks and two-term simple-minded collections under the assumption that the index of the normal subgroup <em>N</em> in <em>G</em> is a <em>p</em>-power.</div></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Clifford's theorem for bricks\",\"authors\":\"Yuta Kozakai , Arashi Sakai\",\"doi\":\"10.1016/j.jalgebra.2024.09.021\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>Let <em>G</em> be a finite group, <em>N</em> a normal subgroup of <em>G</em>, and <em>k</em> a field of characteristic <span><math><mi>p</mi><mo>></mo><mn>0</mn></math></span>. In this paper, we formulate the brick version of Clifford's theorem under suitable assumptions and prove it by using the theory of wide subcategories. As an application of our theorem, we consider the restrictions of semibricks and two-term simple-minded collections under the assumption that the index of the normal subgroup <em>N</em> in <em>G</em> is a <em>p</em>-power.</div></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-10-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0021869324005283\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021869324005283","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
设 G 是有限群，N 是 G 的正则子群，k 是特征 p>0 的域。在本文中，我们在适当的假设条件下提出了砖版克利福德定理，并利用广义子类理论证明了这一定理。作为我们定理的一个应用，我们考虑了在 G 中正态子群 N 的索引是 p 幂的假设下半砖和两期简明集合的限制。
Let G be a finite group, N a normal subgroup of G, and k a field of characteristic . In this paper, we formulate the brick version of Clifford's theorem under suitable assumptions and prove it by using the theory of wide subcategories. As an application of our theorem, we consider the restrictions of semibricks and two-term simple-minded collections under the assumption that the index of the normal subgroup N in G is a p-power.
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