On the existence and number of invariant polynomials

Lucas Reis

On the existence and number of invariant polynomials

Rings and Algebras 2018-11-07 v1

Authors: Lucas Reis

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.

Keywords

invariant polynomials PGL_2 finite fields monic irreducible polynomials fixed points group actions

Cite

@article{arxiv.1811.02537,
  title  = {On the existence and number of invariant polynomials},
  author = {Lucas Reis},
  journal= {arXiv preprint arXiv:1811.02537},
  year   = {2018}
}

Comments

13 pages; overlap with arXiv:1708.06862

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