Raimund Preusser - Chebyshev Laboratory, St. Petersburg State University, Russia

Let K be a field and n\geq ۳. 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_۱,\ldots,i_m\in\{\pm ۱\} such that the product C^{i_۱}\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=۳ or n=\infty.

general linear groups, Conjugacy classes, matrix identities