# Signed symmetric group of finite degree is a Coxeter group

From Groupprops

## Statement

Suppose is a nonnegative integer and is the signed symmetric group of degree . Then, is isomorphic to a Coxeter group with generators , the are as follows:

- for
- if

Under the isomorphism, is idnetified with the transposition and is the diagonal matrix with the last entry and all remaining entries equal to .