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A Generalization of G-Nilpotent Units in Commutative Group Rings to Direct Product Groups

Cilt: 28 Sayı: 1 30 Nisan 2023
Turgut Hanoymak *, Ömer Küsmüş
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A Generalization of G-Nilpotent Units in Commutative Group Rings to Direct Product Groups

Öz

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.

Anahtar Kelimeler

Direct product group, Generalization, Nilpotent, Unit

Kaynakça

  1. Bourbaki, N. (1989). Elements of Mathematics, Commutative Algebra. Berlin, Germany: Springer.
  2. Danchev, P. (2008). Trivial units in commutative group algebras. Extracta mathematicae, 23(1), 49-60.
  3. Danchev, P. (2009). Trivial units in abelian group algebras. Extracta mathematicae, 24(1), 47-53.
  4. Danchev, P. (2010). Idempotent units of commutative group rings. Communications in Algebra, 38(12), 4649-4654. doi:10.1080/00927871003742842
  5. Danchev, P. (2012). G-nilpotent units in Abelian group rings. Commentationes Mathematicae Universitatis Carolinae, 53(2), 179-187.
  6. Görentaş, N. (1999). A characterization of idempotents and idempotent generators of QS_3. Bulletion of pure and Applied Sciences, 2(18), 289-292.
  7. Görentaş, N. (2020). A note on simple trinomial units in U_1 (ZC_p). Turkish Journal of Mathematics, 44(5), 1783-1791. doi:10.3906/mat-2003-63
  8. Karpilovsky, G. (1982). On units in commutative group rings. Archiv der Mathematik, 38, 420–422. doi:10.1007/BF01304809
  9. Küsmüş, Ö. (2019,Aralık). Nilpotent, idempotent and units in group rings. (PhD), Yuzuncu Yıl University, Institute of Natural and Applied Science Van, Turkey.
  10. Küsmüş, Ö. (2020). On idempotent units in commutative group rings. Sakarya University Journal of Science, 24(4), 782-790. doi:10.16984/saufenbilder.733935

Ayrıntılar

Birincil Dil

İngilizce

Konular

-

Bölüm

Araştırma Makalesi

Yazarlar

Erken Görünüm Tarihi

29 Nisan 2023

Yayımlanma Tarihi

30 Nisan 2023

Gönderilme Tarihi

2 Nisan 2022

Kabul Tarihi

29 Ağustos 2022

Yayımlandığı Sayı

Yıl 2023 Cilt: 28 Sayı: 1

DOI

https://doi.org/10.53433/yyufbed.1097581

IZ

https://izlik.org/JA42EK59CF

Kaynak Göster

RIS / Bibtex
APA
Hanoymak, T., & Küsmüş, Ö. (2023). A Generalization of G-Nilpotent Units in Commutative Group Rings to Direct Product Groups. Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 28(1), 8-18. https://doi.org/10.53433/yyufbed.1097581
AMA
1.Hanoymak T, Küsmüş Ö. A Generalization of G-Nilpotent Units in Commutative Group Rings to Direct Product Groups. YYUFBED. 2023;28(1):8-18. doi:10.53433/yyufbed.1097581
Chicago
Hanoymak, Turgut, ve Ömer Küsmüş. 2023. “A Generalization of G-Nilpotent Units in Commutative Group Rings to Direct Product Groups”. Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi 28 (1): 8-18. https://doi.org/10.53433/yyufbed.1097581.
EndNote
Hanoymak T, Küsmüş Ö (01 Nisan 2023) A Generalization of G-Nilpotent Units in Commutative Group Rings to Direct Product Groups. Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi 28 1 8–18.
IEEE
[1]T. Hanoymak ve Ö. Küsmüş, “A Generalization of G-Nilpotent Units in Commutative Group Rings to Direct Product Groups”, YYUFBED, c. 28, sy 1, ss. 8–18, Nis. 2023, doi: 10.53433/yyufbed.1097581.
ISNAD
Hanoymak, Turgut - Küsmüş, Ömer. “A Generalization of G-Nilpotent Units in Commutative Group Rings to Direct Product Groups”. Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi 28/1 (01 Nisan 2023): 8-18. https://doi.org/10.53433/yyufbed.1097581.
JAMA
1.Hanoymak T, Küsmüş Ö. A Generalization of G-Nilpotent Units in Commutative Group Rings to Direct Product Groups. YYUFBED. 2023;28:8–18.
MLA
Hanoymak, Turgut, ve Ömer Küsmüş. “A Generalization of G-Nilpotent Units in Commutative Group Rings to Direct Product Groups”. Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi, c. 28, sy 1, Nisan 2023, ss. 8-18, doi:10.53433/yyufbed.1097581.
Vancouver
1.Turgut Hanoymak, Ömer Küsmüş. A Generalization of G-Nilpotent Units in Commutative Group Rings to Direct Product Groups. YYUFBED. 01 Nisan 2023;28(1):8-18. doi:10.53433/yyufbed.1097581

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

Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi

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