{"title":"On conormal subgroups","authors":"M. Dixon, L. A. Kurdachenko, I. Subbotin","doi":"10.1142/s0218196722500163","DOIUrl":null,"url":null,"abstract":"We introduce the concept of a conormal subgroup: a subgroup is conormal if it is contranormal in its normal closure. This unifies the concepts of normal and contranormal subgroups. We obtain some important properties of conormal subgroups, describe their connections with transitivity of normality, and study groups in which all conormal subgroups are normal.","PeriodicalId":13615,"journal":{"name":"Int. J. Algebra Comput.","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2022-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Int. J. Algebra Comput.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s0218196722500163","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
We introduce the concept of a conormal subgroup: a subgroup is conormal if it is contranormal in its normal closure. This unifies the concepts of normal and contranormal subgroups. We obtain some important properties of conormal subgroups, describe their connections with transitivity of normality, and study groups in which all conormal subgroups are normal.
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