Journal of Group Theory
Editor-in-Chief: Parker, Christopher W.
Managing Editor: Wilson, John S. / Khukhro, Evgenii I. / Kramer, Linus
IMPACT FACTOR 2018: 0.470
5-year IMPACT FACTOR: 0.520
CiteScore 2018: 0.53
SCImago Journal Rank (SJR) 2018: 0.566
Source Normalized Impact per Paper (SNIP) 2018: 1.047
Mathematical Citation Quotient (MCQ) 2018: 0.48
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.
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