On the Unit Group of the Integral Group Ring Z(S_3×C_3)
Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi, cilt.29, sa.1, ss.157-165, 2024 (TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 29 Sayı: 1
- Basım Tarihi: 2024
- Doi Numarası: 10.53433/yyufbed.1361776
- Dergi Adı: Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi
- Derginin Tarandığı İndeksler: TR DİZİN (ULAKBİM)
- Sayfa Sayıları: ss.157-165
- Van Yüzüncü Yıl Üniversitesi Adresli: Hayır
Özet
Abstract: Describing the group of units in the integral group ring is a famous and
classical open problem. Let 𝑆3 and 𝐶3 be the symmetric group of order 6 and a
cyclic group of order 3, respectively. In this paper, a description of the units of
the integral group ring ℤ(𝑆3 × 𝐶3) of the direct product group 𝑆3 × 𝐶3
concerning a complex representation of degree two is given. As a result, a part of
the conjecture which is introduced in (Low, 2008) and related to group rings over
a complex integral domain is resolved using representation theory.