generalized symmetric group

[RobinHankin]

There is a nice generalization of the permutation group. Usually one considers the permutation matrix to have entries 0 and 1, with exactly one non-zero entry in each row and in each column. It is possible to consider the nonzero elements to be any nonzero number, see:

https://en.wikipedia.org/wiki/Generalized_permutation_matrix

It would be nice to consider the generalized symmetric group discussed at https://en.wikipedia.org/wiki/Generalized_symmetric_group