Martin Hertweck, E Iwaki, Eric Jespers, S. O Juriaans
July 26, 2007
For an arbitrary group G , and a G -adapted ring R (for example, R = ℤ), let 𝒰 be the group of units of the group ring RG , and let Z ∞ (𝒰) denote the union of the terms of the upper central series of 𝒰, the elements of which are called hypercentral units. It is shown that Z ∞ (𝒰) ⩽ ( G ). As a consequence, hypercentral units commute with all unipotent elements, and if G has non-normal finite subgroups with R( G ) denoting their intersection, then [𝒰,Z ∞ (𝒰)] ⩽ R( G ). Further consequences are given as well as concrete examples.