{"title":"Değişmeli Grup Halkalarında G-Nilpotent Birimsel Elemanların Direkt Çarpım Gruplarına Bir Genellemesi","authors":"Turgut Hanoymak, Ömer Küsmüş","doi":"10.53433/yyufbed.1097581","DOIUrl":null,"url":null,"abstract":"Let V(RG) denote the normalized unit group of the group ring RG of a group G over a ring R. The concept of G-nilpotent unit in a commutative group ring has been defined in (Danchev 2012). In this study, some necessary and sufficient conditions for a normalized unit group in a commutative group ring of a direct product group G×H to consist only of G×H-nilpotent units have been given and especially some results which are related to groups G×C_3 and G×C_4 have been introduced where C_3 and C_4 are cyclic groups of orders 3 and 4 respectively. In this context, we can say that the paper extends the results in (Danchev,2012). At the end, an open problem is served as a future work.","PeriodicalId":386555,"journal":{"name":"Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2022-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.53433/yyufbed.1097581","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Değişmeli Grup Halkalarında G-Nilpotent Birimsel Elemanların Direkt Çarpım Gruplarına Bir Genellemesi
Let V(RG) denote the normalized unit group of the group ring RG of a group G over a ring R. The concept of G-nilpotent unit in a commutative group ring has been defined in (Danchev 2012). In this study, some necessary and sufficient conditions for a normalized unit group in a commutative group ring of a direct product group G×H to consist only of G×H-nilpotent units have been given and especially some results which are related to groups G×C_3 and G×C_4 have been introduced where C_3 and C_4 are cyclic groups of orders 3 and 4 respectively. In this context, we can say that the paper extends the results in (Danchev,2012). At the end, an open problem is served as a future work.