On products of conjugacy classes in general linear groups

Preusser, Raimund

doi:10.22108/ijgt.2021.123469.1627

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	On products of conjugacy classes in general linear groups
International Journal of Group Theory
مقاله 8، دوره 11، شماره 4، اسفند 2022، صفحه 229-252 اصل مقاله (489.87 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/ijgt.2021.123469.1627
نویسنده
Raimund Preusser^*
Chebyshev Laboratory, St. Petersburg State University, Russia
چکیده
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 $n=\infty$.
کلیدواژه‌ها
general linear groups؛ conjugacy classes؛ matrix identities

مراجع
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On products of conjugacy classes in general linear groups