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

Yilmaz, A.

Istanb. Üniv. Fen Fak. Mat. Derg. 49, 77-84 (1990).

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 \(\mathbb{Z} S_ 3\).

Reviewer: C.Polcino Milies (São Paulo)

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)

Keywords:

symmetric groups; groups of normalized units; doubly stochastic matrices

Citations:

Zbl 0616.16004