Number of irreducible polynomials whose compositions with monic monomials have large irreducible factors

Sabina B. Pannek

Number of irreducible polynomials whose compositions with monic monomials have large irreducible factors

Group Theory 2019-03-27 v1

Authors: Sabina B. Pannek

Abstract

Given a prime power $q$ and positive integers $m,t,e$ with $e > mt/2$ , we determine the number of all monic irreducible polynomials $f(x)$ of degree $m$ with coefficients in $\mathbb{F}_q$ such that $f(x^t)$ contains an irreducible factor of degree $e$ . Polynomials with these properties are important for justifying randomised algorithms for computing with matrix groups.

Keywords

irreducible polynomials monic monomials finite fields irreducible factors matrix groups randomised algorithms

Cite

@article{arxiv.1903.10846,
  title  = {Number of irreducible polynomials whose compositions with monic monomials have large irreducible factors},
  author = {Sabina B. Pannek},
  journal= {arXiv preprint arXiv:1903.10846},
  year   = {2019}
}

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