Martin Hertweck, E Iwaki, Eric Jespers, S. O Juriaans
On hypercentral units in integral group rings
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.
Journal of Group Theory, Walter de Gruyter
Print ISSN: 1433-5883
Volume: 10, 07/2007
Pages: 477 - 504
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