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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].

Groups qui reflètent les décompositions de leurs quotients ou de leurs sous-groups

Khalid Benabdallah, Robert Bradley (1977)

Revista colombiana de matematicas

Growth functions for some uniformly amenable groups

Janusz Dronka, Bronislaw Wajnryb, Paweł Witowicz, Kamil Orzechowski (2017)

Open Mathematics

We present a simple constructive proof of the fact that every abelian discrete group is uniformly amenable. We improve the growth function obtained earlier and find the optimal growth function in a particular case. We also compute a growth function for some non-abelian uniformly amenable group.

Currently displaying 1 – 3 of 3