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

#### Zoom link: us02web.zoom.us/j/86865846431Let $M\geq 2$ be any integer. Consider the set$\text{GL}(n,q)^M=\{x^M|x\in \text{GL}(n,q)\}$, whichis 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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