{"title":"关于群代数的Wedderburn分解的一个注记","authors":"Gaurav Mittal , R.K. Sharma","doi":"10.1016/j.exco.2023.100105","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we extend the result of Mittal and Sharma (Bull. Korean Math. Soc. 2022) on Wedderburn decomposition (WD) of a finite semisimple group algebra. It is known that, under certain conditions, WD of a finite semisimple group algebra <span><math><mrow><msub><mrow><mi>F</mi></mrow><mrow><mi>q</mi></mrow></msub><mi>G</mi></mrow></math></span> can be computed from WD of its subalgebra <span><math><mrow><msub><mrow><mi>F</mi></mrow><mrow><mi>q</mi></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>/</mo><mi>H</mi><mo>)</mo></mrow></mrow></math></span>, where <span><math><mi>H</mi></math></span> is a normal subgroup of <span><math><mi>G</mi></math></span> of prime order and <span><math><mrow><mi>q</mi><mo>=</mo><msup><mrow><mi>p</mi></mrow><mrow><mi>k</mi></mrow></msup></mrow></math></span> for some prime <span><math><mi>p</mi></math></span> and positive integer <span><math><mi>k</mi></math></span>. We extend this result to any normal subgroup <span><math><mi>H</mi></math></span> of <span><math><mi>G</mi></math></span> of order <span><math><mi>n</mi></math></span>.</p></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"3 ","pages":"Article 100105"},"PeriodicalIF":0.0000,"publicationDate":"2023-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A short note on Wedderburn decomposition of a group algebra\",\"authors\":\"Gaurav Mittal , R.K. Sharma\",\"doi\":\"10.1016/j.exco.2023.100105\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we extend the result of Mittal and Sharma (Bull. Korean Math. Soc. 2022) on Wedderburn decomposition (WD) of a finite semisimple group algebra. It is known that, under certain conditions, WD of a finite semisimple group algebra <span><math><mrow><msub><mrow><mi>F</mi></mrow><mrow><mi>q</mi></mrow></msub><mi>G</mi></mrow></math></span> can be computed from WD of its subalgebra <span><math><mrow><msub><mrow><mi>F</mi></mrow><mrow><mi>q</mi></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>/</mo><mi>H</mi><mo>)</mo></mrow></mrow></math></span>, where <span><math><mi>H</mi></math></span> is a normal subgroup of <span><math><mi>G</mi></math></span> of prime order and <span><math><mrow><mi>q</mi><mo>=</mo><msup><mrow><mi>p</mi></mrow><mrow><mi>k</mi></mrow></msup></mrow></math></span> for some prime <span><math><mi>p</mi></math></span> and positive integer <span><math><mi>k</mi></math></span>. We extend this result to any normal subgroup <span><math><mi>H</mi></math></span> of <span><math><mi>G</mi></math></span> of order <span><math><mi>n</mi></math></span>.</p></div>\",\"PeriodicalId\":100517,\"journal\":{\"name\":\"Examples and Counterexamples\",\"volume\":\"3 \",\"pages\":\"Article 100105\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-04-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Examples and Counterexamples\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S2666657X23000071\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Examples and Counterexamples","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2666657X23000071","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A short note on Wedderburn decomposition of a group algebra
In this paper, we extend the result of Mittal and Sharma (Bull. Korean Math. Soc. 2022) on Wedderburn decomposition (WD) of a finite semisimple group algebra. It is known that, under certain conditions, WD of a finite semisimple group algebra can be computed from WD of its subalgebra , where is a normal subgroup of of prime order and for some prime and positive integer . We extend this result to any normal subgroup of of order .
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