On the existence and number of invariant polynomials

Abstract

This paper explores a natural action of the group ${\mathrm{PGL}}_2({\mathbb{F}}_q)$ on the set of monic irreducible polynomials of degree at least two over a finite field ${\mathbb{F}}_q$. Our main results deal with the existence and number of fixed points and, in particular, we provide some improvements of previous works.

13 pages; overlap with arXiv:1708.06862