{"title":"多项式时间有限群的形成:f -残差和f -次正态","authors":"Viachaslau I. Murashka","doi":"10.1016/j.jsc.2023.102271","DOIUrl":null,"url":null,"abstract":"<div><p>For a wide family of formations <span><math><mi>F</mi></math></span> it is proved that the <span><math><mi>F</mi></math></span><span>-residual of a permutation<span> finite group can be computed in polynomial time. Moreover, if in the previous case </span></span><span><math><mi>F</mi></math></span> is hereditary, then the <span><math><mi>F</mi></math></span>-subnormality of a subgroup can be checked in polynomial time.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Formations of finite groups in polynomial time: F-residuals and F-subnormality\",\"authors\":\"Viachaslau I. Murashka\",\"doi\":\"10.1016/j.jsc.2023.102271\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>For a wide family of formations <span><math><mi>F</mi></math></span> it is proved that the <span><math><mi>F</mi></math></span><span>-residual of a permutation<span> finite group can be computed in polynomial time. Moreover, if in the previous case </span></span><span><math><mi>F</mi></math></span> is hereditary, then the <span><math><mi>F</mi></math></span>-subnormality of a subgroup can be checked in polynomial time.</p></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2023-09-25\",\"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/S0747717123000858\",\"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/S0747717123000858","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Formations of finite groups in polynomial time: F-residuals and F-subnormality
For a wide family of formations it is proved that the -residual of a permutation finite group can be computed in polynomial time. Moreover, if in the previous case is hereditary, then the -subnormality of a subgroup can be checked in polynomial time.
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