Cosets of centralizers in the general linear group contain regular elements Original Research Article

Let K be an infinite field of arbitrary characteristic. Ifa set membership, variant G colon, equalsGLn(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 GLn(K) is important for the study of the representation varieties of fundamental groups of compact orientable surfaces.