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 $u$.References
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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