{"title":"有限群中的集合Kp","authors":"A. I. Zabarina, E. A. Fomina","doi":"10.17223/19988621/81/1","DOIUrl":null,"url":null,"abstract":"The study of the properties of the set Kp consisting of elements of a non-Abelian group that commute with exactly p elements of the group G is continued. In particular, this question is considered for groups of order p1p2...pk, k ≥ 3 and p2q, where рі, q are prime numbers. It is also proved that the set K5 is non-empty in the three-dimensional projective special linear group. This group has the same order as the alternating group A8, in which the set K5 is empty.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The set Kp in some finite groups\",\"authors\":\"A. I. Zabarina, E. A. Fomina\",\"doi\":\"10.17223/19988621/81/1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The study of the properties of the set Kp consisting of elements of a non-Abelian group that commute with exactly p elements of the group G is continued. In particular, this question is considered for groups of order p1p2...pk, k ≥ 3 and p2q, where рі, q are prime numbers. It is also proved that the set K5 is non-empty in the three-dimensional projective special linear group. This group has the same order as the alternating group A8, in which the set K5 is empty.\",\"PeriodicalId\":43729,\"journal\":{\"name\":\"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.17223/19988621/81/1\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MECHANICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.17223/19988621/81/1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MECHANICS","Score":null,"Total":0}
The study of the properties of the set Kp consisting of elements of a non-Abelian group that commute with exactly p elements of the group G is continued. In particular, this question is considered for groups of order p1p2...pk, k ≥ 3 and p2q, where рі, q are prime numbers. It is also proved that the set K5 is non-empty in the three-dimensional projective special linear group. This group has the same order as the alternating group A8, in which the set K5 is empty.
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