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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Central units of the integral group ring ${{\Bbb {Z}}}A_{5}$


Authors: Yuanlin Li and M. M. Parmenter
Journal: Proc. Amer. Math. Soc. 125 (1997), 61-65
MSC (1991): Primary 16U60, 20C05
MathSciNet review: 1353390
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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

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03626-5
PII: S 0002-9939(97)03626-5
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
Article copyright: © Copyright 1997 American Mathematical Society