## A note on the unit group of $$\mathbb{Z} S_ 4$$.(English)Zbl 0799.16025

This paper characterizes the group of normalized units of $$\mathbb{Z} S_ 4$$ as the group of doubly stochastic matrices in $$\text{GL}(4,\mathbb{Z})$$ using techniques similar to those of P. J. Allen and C. Hobby [Proc. Am. Math. Soc. 99, 9-14 (1987; Zbl 0616.16004)] who studied the units of $$\mathbb{Z} S_ 3$$.

### MSC:

 16U60 Units, groups of units (associative rings and algebras) 16S34 Group rings 20C05 Group rings of finite groups and their modules (group-theoretic aspects)

Zbl 0616.16004