Değişmeli Grup Halkalarında G-Nilpotent Birimsel Elemanların Direkt Çarpım Gruplarına Bir Genellemesi

Author:

HANOYMAK Turgut1,KÜSMÜŞ Ömer2

Affiliation:

1. Van Yuzuncu Yil University

2. VAN YÜZÜNCÜ YIL ÜNİVERSİTESİ

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.

Publisher

Van Yuzuncu Yil University

Reference13 articles.

1. Bourbaki, N., 1989. Commutative Algebra, Chapters 1-7, Elements of Mathematics (Berlin), Springer, Berlin. 625.

2. Danchev P., 2008. Trivial units in commutative group algebras. Extr. Math., 23, 49-60.

3. Danchev P., 2009. Trivial units in abelian group algebras. Extr. Math., 24, 47-53.

4. Danchev P., 2010. Idempotent units of commutative group rings. Commun. Algebra, 38, 4649-4654.

5. Danchev P., 2012. G-nilpotent units in Abelian group rings. Comment. Math. Univ. Carolin., 53(2), 179-187.

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1. On the Unit Group of the Integral Group Ring Z(S_3×C_3);Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi;2024-04-30

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