COSETS OF CENTRALIZERS IN THE GENERAL LINEAR GROUP CONTAIN REGULAR ELEMENTS

Let K be an infinite field of arbitrary characteristic. If a is an ele ment of G = GL(n)(K), we show that every coset of the centralizer of a in G contains a regular element, i.e., a matrix for which the minimal and characteristic polynomials coincide. This property of GL(n)(K) is important for the study of the representation varieties of fundamenta l groups of compact orientable surfaces.