On products of conjugacy classes in general linear groups

Let K be a field and n\geq 3. Let E_n(K)\leq H\leq GL_n(K) be an intermediate group and C a noncentral H-class. Define m(C) as the minimal positive integer m such that \exists i_1,\ldots,i_m\in\{\pm 1\} such that the product C^{i_1}\cdots C^{i_m} contains all nontrivial elementary transvections. In this article we obtain a sharp upper bound for m(C). Moreover, we determine m(C) for any noncentral H-class C under the assumption that K is algebraically closed or n=3 or n=\infty.

On products of conjugacy classes in general linear groups Keywords:

general linear groups , Conjugacy classes , matrix identities