A one-parameter family of degree 36 polynomials with PSp(6,2) as Galois group over Q(t)

TL;DR

This paper constructs a one-parameter family of degree 36 polynomials over Q(t) whose Galois group is the symplectic group PSp(6,2), illustrating a specific realization of this group as a Galois group over the rationals.

Contribution

It introduces a new explicit family of polynomials with Galois group PSp(6,2) over Q(t), expanding known examples of Galois realizations for this group.

Findings

Explicit family of degree 36 polynomials with Galois group PSp(6,2)

Demonstrates realization of PSp(6,2) as a Galois group over Q(t)

Provides a method for constructing similar Galois extensions

Abstract

We present a one-parameter family of degree 36 polynomials with the symplectic 2-transitive group PSp(6,2) as Galois group over Q(t).