On the affine Weyl group of type \(\tilde A_{n-1}\)
The author proves that the Weyl group \(\tilde A_{n-1}\) is a split extension of \(S_ n\) by a direct product of (n-1) copies of Z. The center is trivial for \(n>4\). Also, \(\tilde A_{3-1}\) and \(\tilde A_{4- 1}\) are solvable of length 3 and 4 respectively. For \(n>4\), the first and second derived groups are identical.
scientific article; zbMATH DE number 4031952