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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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Central units of the integral group ring $\mathbb {Z}A_5$
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by Yuanlin Li and M. M. Parmenter PDF
Proc. Amer. Math. Soc. 125 (1997), 61-65 Request permission

Abstract:

There are very few cases known of nonabelian groups $G$ where the group of central units of $\mathbb { Z}G$, denoted $Z(U(\mathbb { Z}G))$, is nontrivial and where the structure of $Z(U(\mathbb { Z}G))$, including a complete set of generators, has been determined. In this note, we show that the central units of augmentation 1 in the integral group ring $\mathbb {Z }A_5$ form an infinite cyclic group $\langle u \rangle$, and we explicitly find the generator $u$.
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Additional Information
  • Yuanlin Li
  • Affiliation: Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, Newfoundland, Canada A1C 5S7
  • Email: yuanlin@fermat.math.mun.ca
  • M. M. Parmenter
  • Affiliation: Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, Newfoundland, Canada A1C 5S7
  • Email: mparmen@plato.ucs.mun.ca
  • Received by editor(s): July 22, 1995
  • Additional Notes: The second author was supported in part by NSERC grant A8775.
  • Communicated by: Ronald M. Solomon
  • © Copyright 1997 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 125 (1997), 61-65
  • MSC (1991): Primary 16U60, 20C05
  • DOI: https://doi.org/10.1090/S0002-9939-97-03626-5
  • MathSciNet review: 1353390