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

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 $u$.