Araştırma Makalesi

On the Unit Group of the Integral Group Ring Z(S_3×C_3)

Cilt: 29 Sayı: 1 30 Nisan 2024
Ömer Küsmüş *, İsmail Denizler , Richard M. Low
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On the Unit Group of the Integral Group Ring Z(S_3×C_3)

Öz

Describing the group of units in the integral group ring is a famous and classical open problem. Let S_3 and C_3 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(S_3×C_3) of the direct product group S_3×C_3 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.

Anahtar Kelimeler

Complex representation, Cyclic group, Direct product group, Group rings, Integral group rings, Symmetric group

Kaynakça

  1. Bilgin, T., Küsmüş, Ö., & Low, R. M. (2016). A characterization of the unit group in Z[T×C_2]. Bulletin of the Korean Mathematical Society, 53(4), 1105-1112. doi:10.4134/BKMS.b150526
  2. Eisele, F., Kiefer, A., & Gelder, I. V. (2015). Describing units of integral group rings up to commensurability. Journal of Pure and Applied Algebra, 219(7), 2901-2916. doi:10.1016/j.jpaa.2014.09.031
  3. Hanoymak, T., & Küsmüş, Ö. (2023). A generalization of G-nilpotent units in commutative group rings to direct product groups. Yuzuncu Yil University Journal of the Institute of Natural and Applied Sciences, 28(1), 8-18. doi:10.53433/yyufbed.1097581
  4. Jespers, E., & Parmenter, M. M. (1992). Bicyclic units in ZS_3. Bulletin of the Belgium Mathematical Society, 44, 141-146.
  5. Jespers, E., & Parmenter, M. M. (1993). Units of group rings of groups of order 16. Glasgow Mathematical Journal, 35, 367-379. doi:10.1017/S0017089500009952
  6. Jespers, E. (1995). Bicyclic units in some integral group rings. Canadian Mathematics Bulletin, 38(1), 80-86. doi:10.4153/CMB-1995-010-4
  7. Jespers, E., & del Rio, A. (2016). Group Ring Groups. Vol. 1 and 2. Berlin, Germany: De Gruyter.
  8. Kelebek, I. G., & Bilgin, T. (2014). Characterization of U_1 (Z[C_n×K_4]). European Journal of Pure and Applied Mathematics, 7(4), 462-471.
  9. Küsmüş, Ö. (2020). On idempotent units in commutative group rings. Sakarya University Journal of Science, 24(4), 782-790. doi:10.16984/saufenbilder.733935
  10. Low, R. M. (1998). Units in integral group rings for direct products. (PhD), Western Michigan University, Kalamazoo, MI.

Ayrıntılar

Birincil Dil

İngilizce

Konular

Cebir ve Sayı Teorisi

Bölüm

Araştırma Makalesi

Yazarlar

Yayımlanma Tarihi

30 Nisan 2024

Gönderilme Tarihi

18 Eylül 2023

Kabul Tarihi

18 Aralık 2023

Yayımlandığı Sayı

Yıl 2024 Cilt: 29 Sayı: 1

DOI

https://doi.org/10.53433/yyufbed.1361776

IZ

https://izlik.org/JA28ZE97XY

Kaynak Göster

RIS / Bibtex
APA
Küsmüş, Ö., Denizler, İ., & Low, R. M. (2024). On the Unit Group of the Integral Group Ring Z(S_3×C_3). Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 29(1), 157-165. https://doi.org/10.53433/yyufbed.1361776
AMA
1.Küsmüş Ö, Denizler İ, Low RM. On the Unit Group of the Integral Group Ring Z(S_3×C_3). YYUFBED. 2024;29(1):157-165. doi:10.53433/yyufbed.1361776
Chicago
Küsmüş, Ömer, İsmail Denizler, ve Richard M. Low. 2024. “On the Unit Group of the Integral Group Ring Z(S_3×C_3)”. Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi 29 (1): 157-65. https://doi.org/10.53433/yyufbed.1361776.
EndNote
Küsmüş Ö, Denizler İ, Low RM (01 Nisan 2024) On the Unit Group of the Integral Group Ring Z(S_3×C_3). Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi 29 1 157–165.
IEEE
[1]Ö. Küsmüş, İ. Denizler, ve R. M. Low, “On the Unit Group of the Integral Group Ring Z(S_3×C_3)”, YYUFBED, c. 29, sy 1, ss. 157–165, Nis. 2024, doi: 10.53433/yyufbed.1361776.
ISNAD
Küsmüş, Ömer - Denizler, İsmail - Low, Richard M. “On the Unit Group of the Integral Group Ring Z(S_3×C_3)”. Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi 29/1 (01 Nisan 2024): 157-165. https://doi.org/10.53433/yyufbed.1361776.
JAMA
1.Küsmüş Ö, Denizler İ, Low RM. On the Unit Group of the Integral Group Ring Z(S_3×C_3). YYUFBED. 2024;29:157–165.
MLA
Küsmüş, Ömer, vd. “On the Unit Group of the Integral Group Ring Z(S_3×C_3)”. Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi, c. 29, sy 1, Nisan 2024, ss. 157-65, doi:10.53433/yyufbed.1361776.
Vancouver
1.Ömer Küsmüş, İsmail Denizler, Richard M. Low. On the Unit Group of the Integral Group Ring Z(S_3×C_3). YYUFBED. 01 Nisan 2024;29(1):157-65. doi:10.53433/yyufbed.1361776