{"title":"广义二面体ci群","authors":"Ted Dobson, M. Muzychuk, Pablo Spiga","doi":"10.26493/1855-3974.2443.02e","DOIUrl":null,"url":null,"abstract":"In this paper, we find a strong new restriction on the structure of CI-groups. We show that, if $R$ is a generalised dihedral group and if $R$ is a CI-group, then for every odd prime $p$ the Sylow $p$-subgroup of $R$ has order $p$, or $9$. Consequently, any CI-group with quotient a generalised dihedral group has the same restriction, that for every odd prime $p$ the Sylow $p$-subgroup of the group has order $p$, or $9$. We also give a counter example to the conjecture that every BCI-group is a CI-group.","PeriodicalId":8402,"journal":{"name":"Ars Math. Contemp.","volume":"18 1","pages":"2"},"PeriodicalIF":0.0000,"publicationDate":"2020-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":"{\"title\":\"Generalized dihedral CI-groups\",\"authors\":\"Ted Dobson, M. Muzychuk, Pablo Spiga\",\"doi\":\"10.26493/1855-3974.2443.02e\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we find a strong new restriction on the structure of CI-groups. We show that, if $R$ is a generalised dihedral group and if $R$ is a CI-group, then for every odd prime $p$ the Sylow $p$-subgroup of $R$ has order $p$, or $9$. Consequently, any CI-group with quotient a generalised dihedral group has the same restriction, that for every odd prime $p$ the Sylow $p$-subgroup of the group has order $p$, or $9$. We also give a counter example to the conjecture that every BCI-group is a CI-group.\",\"PeriodicalId\":8402,\"journal\":{\"name\":\"Ars Math. Contemp.\",\"volume\":\"18 1\",\"pages\":\"2\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-08-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Ars Math. Contemp.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.26493/1855-3974.2443.02e\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Ars Math. Contemp.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.26493/1855-3974.2443.02e","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In this paper, we find a strong new restriction on the structure of CI-groups. We show that, if $R$ is a generalised dihedral group and if $R$ is a CI-group, then for every odd prime $p$ the Sylow $p$-subgroup of $R$ has order $p$, or $9$. Consequently, any CI-group with quotient a generalised dihedral group has the same restriction, that for every odd prime $p$ the Sylow $p$-subgroup of the group has order $p$, or $9$. We also give a counter example to the conjecture that every BCI-group is a CI-group.
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