{"title":"原始字符的零","authors":"Wenyang Wang null, N. Du","doi":"10.4208/jms.v55n1.22.05","DOIUrl":null,"url":null,"abstract":". Let G be a finite group. An irreducible character χ of G is said to be primitive if χ 6 = ϑ G for any character ϑ of a proper subgroup of G . In this paper, we consider about the zeros of primitive characters. Denote by Irr pri ( G ) the set of all irreducible primitive characters of G . We proved that if g ∈ G and the order of gG ′ in the factor group G / G ′ does not divide | Irr pri ( G ) | , then there exists ϕ ∈ Irr pri ( G ) such that ϕ ( g )= 0.","PeriodicalId":43526,"journal":{"name":"数学研究","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Zeros of Primitive Characters\",\"authors\":\"Wenyang Wang null, N. Du\",\"doi\":\"10.4208/jms.v55n1.22.05\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". Let G be a finite group. An irreducible character χ of G is said to be primitive if χ 6 = ϑ G for any character ϑ of a proper subgroup of G . In this paper, we consider about the zeros of primitive characters. Denote by Irr pri ( G ) the set of all irreducible primitive characters of G . We proved that if g ∈ G and the order of gG ′ in the factor group G / G ′ does not divide | Irr pri ( G ) | , then there exists ϕ ∈ Irr pri ( G ) such that ϕ ( g )= 0.\",\"PeriodicalId\":43526,\"journal\":{\"name\":\"数学研究\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2022-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"数学研究\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4208/jms.v55n1.22.05\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"数学研究","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4208/jms.v55n1.22.05","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
. Let G be a finite group. An irreducible character χ of G is said to be primitive if χ 6 = ϑ G for any character ϑ of a proper subgroup of G . In this paper, we consider about the zeros of primitive characters. Denote by Irr pri ( G ) the set of all irreducible primitive characters of G . We proved that if g ∈ G and the order of gG ′ in the factor group G / G ′ does not divide | Irr pri ( G ) | , then there exists ϕ ∈ Irr pri ( G ) such that ϕ ( g )= 0.
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