University of Isfahan International Journal of Group Theory 2251-7650 11 4 2022 12 01 On products of conjugacy classes in general linear groups 229 252 26036 10.22108/ijgt.2021.123469.1627 EN Raimund Preusser Chebyshev Laboratory, St. Petersburg State University, Russia Journal Article 2020 06 11 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 $n=\infty$. https://ijgt.ui.ac.ir/article_26036_36aaaeb1e50575a14d9de67d71f69ab6.pdf