Realizing cyclic linear transformations as Frobenius elements in the Galois groups of $q$-polynomials over function fields

Rod Gow; Gary McGuire

Realizing cyclic linear transformations as Frobenius elements in the Galois groups of $q$-polynomials over function fields

Number Theory 2024-02-13 v2

Authors: Rod Gow , Gary McGuire

Abstract

We realize Frobenius conjugacy classes in Galois groups of certain $q$ -polynomials over $\mathbb{F}_q(t)$ using specific degree 1 ideals. We combine this with methods from elementary linear algebra and group theory to realize transvections in some linear Galois groups. This enables the Galois group to be identified as a known classical group in several reasonably general cases.

Keywords

galois theory frobenius algebra conjugacy classes in groups

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@article{arxiv.2309.00880,
  title  = {Realizing cyclic linear transformations as Frobenius elements in the Galois groups of $q$-polynomials over function fields},
  author = {Rod Gow and Gary McGuire},
  journal= {arXiv preprint arXiv:2309.00880},
  year   = {2024}
}

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This updates and extends an earlier version, including a new title and abstract

Realizing cyclic linear transformations as Frobenius elements in the Galois groups of $q$-polynomials over function fields

Abstract

Keywords

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