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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)

Citations:

Zbl 0616.16004
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