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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
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Source Normalized Impact per Paper (SNIP) 2018: 1.047

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Online
ISSN
1435-4446
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Volume 10, Issue 4

Issues

On hypercentral units in integral group rings

Martin Hertweck
  • Universität Stuttgart, Fachbereich Mathematik, Institut für Geometrie und Topologie, Pfaenwaldring 57, 70550 Stuttgart, Germany.
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/ E Iwaki
  • Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, São Paulo, CEP 05315-970–Brazil.
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/ Eric Jespers / S. O Juriaans
  • Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, São Paulo, CEP 05315-970–Brazil.
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Published Online: 2007-07-26 | DOI: https://doi.org/10.1515/JGT.2007.040

Abstract

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.

About the article


Received: 2006-08-30

Revised: 2006-12-14

Published Online: 2007-07-26

Published in Print: 2007-07-20


Citation Information: Journal of Group Theory, Volume 10, Issue 4, Pages 477–504, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: https://doi.org/10.1515/JGT.2007.040.

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