On products of conjugacy classes in general linear groups

Author(s):

Raimund Preusser *

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:
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 $n=\infty$.
Keywords:

general linear groups , Conjugacy classes , matrix identities

Language:
English
Published:
International Journal of Group Theory, Volume:11 Issue: 4, Dec 2022
Pages:
229 to 252
https://magiran.com/p2529696