A Generalization of G-Nilpotent Units in Commutative Group Rings to Direct Product Groups
Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi, cilt.28, sa.1, ss.8-18, 2023 (TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 28 Sayı: 1
- Basım Tarihi: 2023
- Doi Numarası: 10.53433/yyufbed.1097581
- Dergi Adı: Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi
- Derginin Tarandığı İndeksler: TR DİZİN (ULAKBİM)
- Sayfa Sayıları: ss.8-18
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Van Yüzüncü Yıl Üniversitesi Adresli: Evet
Özet
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.