Thursday, September 24 2020
14:00 - 15:30

IMSc Webinar

Generating function for the powers in $\text{GL}(n,q)$

Rijubrata Kundu


Zoom link:

Let $M\geq 2$ be any integer. Consider the set
$\text{GL}(n,q)^M=\{x^M|x\in \text{GL}(n,q)\}$, which
is the set of all $M^{th}$ powers in the group $\text{GL}(n,q)$. In this talk, we will obtain generating functions for

(a) the proportion of regular and regular semsimple elements in
$\text{GL}(n,q)^M$, assuming $(M,q)=1$,

(b) the proportion of semisimple and all elements which are $M^{th}$ powers when $(M,q)=1$, and $M$ is a power of a prime.

Time permitting we will also discuss the other extreme, where we assume $M$ is a prime and $q$ is a power of $M$.

This is a joint work with Dr. Anupam Singh.

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