{"title":"模群代数的单位群的幂零类的注记","authors":"F. Catino, S. Siciliano, Ernesto Spinelli","doi":"10.3318/PRIA.2008.108.1.65","DOIUrl":null,"url":null,"abstract":"It is well known that a modular group algebra KG is Lie nilpotent if, and only if, its unit group U(KG) is nilpotent. In this note we prove that if G is a torsion group, then the equality cIl(KG) = c'(U(KG)) occurs.","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"6 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"A NOTE ON THE NILPOTENCY CLASS OF THE UNIT GROUP OF A MODULAR GROUP ALGEBRA\",\"authors\":\"F. Catino, S. Siciliano, Ernesto Spinelli\",\"doi\":\"10.3318/PRIA.2008.108.1.65\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"It is well known that a modular group algebra KG is Lie nilpotent if, and only if, its unit group U(KG) is nilpotent. In this note we prove that if G is a torsion group, then the equality cIl(KG) = c'(U(KG)) occurs.\",\"PeriodicalId\":434988,\"journal\":{\"name\":\"Mathematical Proceedings of the Royal Irish Academy\",\"volume\":\"6 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Proceedings of the Royal Irish Academy\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3318/PRIA.2008.108.1.65\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Proceedings of the Royal Irish Academy","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3318/PRIA.2008.108.1.65","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A NOTE ON THE NILPOTENCY CLASS OF THE UNIT GROUP OF A MODULAR GROUP ALGEBRA
It is well known that a modular group algebra KG is Lie nilpotent if, and only if, its unit group U(KG) is nilpotent. In this note we prove that if G is a torsion group, then the equality cIl(KG) = c'(U(KG)) occurs.
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