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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Finitely generated group ring units
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by Łukasz Wiechecki PDF
Proc. Amer. Math. Soc. 127 (1999), 51-55 Request permission

Abstract:

We give a classification of nilpotent groups $G$ for which the unit group of the integral group ring is finitely generated.
References
  • M. I. Kargapolov and Ju. I. Merzljakov, Fundamentals of the theory of groups, Graduate Texts in Mathematics, vol. 62, Springer-Verlag, New York-Berlin, 1979. Translated from the second Russian edition by Robert G. Burns. MR 551207
  • Z. Marciniak and S. K. Sehgal, Zassenhaus conjectures for infinite groups, Proceedings of the International Conference on Ring Theory, Miskolc ’96, to appear.
  • Maciej Mirowicz, Units in group rings of the infinite dihedral group, Canad. Math. Bull. 34 (1991), no. 1, 83–89. MR 1108933, DOI 10.4153/CMB-1991-013-4
  • Sudarshan K. Sehgal, Topics in group rings, Monographs and Textbooks in Pure and Applied Mathematics, vol. 50, Marcel Dekker, Inc., New York, 1978. MR 508515
  • S. K. Sehgal, Units in integral group rings, Pitman Monographs and Surveys in Pure and Applied Mathematics, vol. 69, Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1993. With an appendix by Al Weiss. MR 1242557
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Additional Information
  • Łukasz Wiechecki
  • Affiliation: Institute of Mathematics, Warsaw University, ul. Banacha 2, 02-097 Warszawa, Poland
  • Email: lwiech@mimuw.edu.pl
  • Received by editor(s): May 12, 1997
  • Communicated by: Ronald M. Solomon
  • © Copyright 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 127 (1999), 51-55
  • MSC (1991): Primary 16S34, 20C07
  • DOI: https://doi.org/10.1090/S0002-9939-99-04823-6
  • MathSciNet review: 1486758