Alladi Ramakrishnan Hall

Counting Conjugacy Classes of Tuples of Commuting Elements in a Finite Group

Amritanshu Prasad

IMSc

Let $G$ be a finite group. Let $c_k$ denote the number of simultaneous conjugacy classes of $k$-tuples of commuting elements in $G$.
We will prove that the generating function $\sum_{k=0}^\infty c_k t^k$ is rational.