论文标题
在$ \ text {gl}（n，q）$中生成功能的功能
Generating functions for the powers in $\text{GL}(n,q)$
论文作者
论文摘要
考虑所有功能的集合$ \ text {gl}（n，q）^m = \ {x^m \ mid x \ in \ in \ text {gl}（n，q）\} $，用于整数$ m \ geq 2 $。在本文中，我们旨在列举定期的，常规的半圣事和半圣像元素以及集合中的共轭类别，即$ \ text {gl}（n，q）^m $，即，这些类型的元素或类别是$ m^{th} $ powers。当$（q，q，m）= 1 $，（ii）半元素和所有元素（和类）时，当$（q，m）= 1 $，（ii）时，我们将获得（i）常规和常规半圣经元素（和班级）的生成功能，当$ m $是质量的功率，$（q，m）= 1 $，（q，m）= 1 $，而（iii）对于$ m $是$ m $ as prime和$ q $ $ $ $ $ m $ $ m $。
Consider the set of all powers $\text{GL}(n ,q)^M = \{x^M \mid x\in \text{GL}(n, q)\}$ for an integer $M\geq 2$. In this article, we aim to enumerate the regular, regular semisimple and semisimple elements as well as conjugacy classes in the set $\text{GL}(n, q)^M$, i.e., the elements or classes of these kinds which are $M^{th}$ powers. We get the generating functions for (i) regular and regular semisimple elements (and classes) when $(q,M)=1$, (ii) for semisimple elements and all elements (and classes) when $M$ is a prime power and $(q,M)=1$, and (iii) for all kinds when $M$ is a prime and $q$ is a power of $M$.
