Cosets of centralizers in the general linear group contain regular elements (Q1893083)

An element in the general linear group is called regular or nonderogatory if its minimal and characteristic polynomials coincide. The author shows, if \(a\) is an element in the general linear group \(\text{GL}(n,K)\), where the field \(K\) is infinite, then every coset of the centralizer of \(a\) contains a regular element.