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Central units of the integral group ring
Authors:Yuanlin Li   M. M. Parmenter
Affiliation:Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, Newfoundland, Canada A1C 5S7 ; Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, Newfoundland, Canada A1C 5S7
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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