The width of the group \(\mathrm{GL}(6,K)\) with respect to a set of quasiroot elements. (Q499392)

Let \(K\) be a field. The structure of \(\mathrm{GL}(6,K)\) with respect to a certain family of conjugacy classes the elements of which are said to be \textit{quasiroot} is studied. Namely, it is proved that any element of \(\mathrm{GL}(6,K) \) is a product of three quasiroot elements, and a complete description of the elements that are products of two quasiroot elements is given. The result arises in studying the width of the exceptional groups of type \(E_6\), but is also of independent interest.