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$G$ -nilpotent units of commutative group rings

Peter Vassilev Danchev (2012)

Commentationes Mathematicae Universitatis Carolinae

Suppose $R$ is a commutative unital ring and $G$ is an abelian group. We give a general criterion only in terms of $R$ and $G$ when all normalized units in the commutative group ring $R G$ are $G$ -nilpotent. This extends recent results published in [Extracta Math., 2008–2009] and [Ann. Sci. Math. Québec, 2009].

Generalised Magnus modules over the braid group.

Mirko Lüdde (1996)

Mathematische Annalen

Generalizations of morphic group rings.

Zan, Libo, Chen, Jianlong, Huang, Qinghe (2007)

International Journal of Mathematics and Mathematical Sciences

Group algebras of abelian groups

Donna Beers, Fred Richman, Elbert A. Walker (1983)

Rendiconti del Seminario Matematico della Università di Padova

Group rings and irreducible representations of space groups.

W. Plesken, W. Hanrath (1985)

Journal für die reine und angewandte Mathematik

Group rings with FC-nilpotent unit groups.

Vikas Bist (1991)

Publicacions Matemàtiques

Let U(RG) be the unit group of the group ring RG. Groups G such that U(RG) is FC-nilpotent are determined, where R is the ring of integers Z or a field K of characteristic zero.

Group Rings with Units Torsion Over the Center.

S.K. Sehgal, G.H. Cliff (1980/1981)

Manuscripta mathematica