论文标题
关于一般线性组中的共轭类产品
On products of conjugacy classes in general linear groups
论文作者
论文摘要
令$ k $为一个字段，$ n \ geq 3 $。令$ e_n（k）\ leq h \ leq gl_n（k）$为中间组，$ c $ a非中心$ h $ class。将$ m（c）$定义为最小的正整数$ m $，以使$ \存在i_1，\ dots，i_m \ in \ {\ pm 1 \} $，这样产品$ c^{i_1} \点c^{i_1} \ dots c^{i_m} $都包含所有非trivirivial emlementary Transvections。在本文中，我们获得了$ m（c）$的锋利上限。此外，我们确定$ m（c）$对于任何非中心$ h $ class $ c $，假设$ k $是代数关闭或$ n = 3 $或$ n = \ n = \ infty $。
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 $\exists i_1,\dots,i_m\in\{\pm 1\}$ such that the product $C^{i_1}\dots C^{i_m}$ 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 $n=\infty$.
