On intersective polynomials with non-solvable Galois group

DOI10.1080/00927872.2017.1385077zbMATH Open1439.11280arXiv1605.07802OpenAlexW2963283511MaRDI QIDQ4570911

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Publication date: 10 July 2018

Published in: (Search for Journal in Brave)

Abstract: We present new theoretical results on the existence of intersective polynomials with certain prescribed Galois groups, namely the projective and affine linear groups $PG{L}_2(ell)$ and $AG{L}_2(ell)$ as well as the affine symplectic groups $AGS{p}_4(ell):=(mathbb{F}_{e}ll{)}^{4}timesGS{p}_4(ell)$. For further families of affine groups, existence results are proven conditional on the existence on certain tamely ramified Galois extensions. We also compute explicit families of intersective polynomials for certain non-solvable groups.

Full work available at URL: https://arxiv.org/abs/1605.07802

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