62 citations · 237 across the 40 of their papers we have counts for
45 papers
On Galois groups of linearized polynomials related to the general linear group of prime degree
Rod Gow, Gary McGuire
Let be any -linearized polynomial with coefficients in , of degree . We consider the Galois group of over , where is tra…
Linearized Polynomials, Galois Groups and Symmetric Power Modules
Rod Gow, Gary McGuire
We investigate some Galois groups of linearized polynomials over fields such as . The space of roots of such a polynomial is a module for its Galois group. We pres…
On Galois groups of linearized polynomials related to the special linear group of prime degree
Rod Gow, Gary McGuire
Let be a field of prime characteristic and let be a power of . We assume that contains the finite field of order . A -polynomial over is an element…
On the realization of subgroups of , and their automorphism groups, as Galois groups over function fields
Rod Gow, Gary McGuire
Let be any field. We give a short and elementary proof that any finite subgroup of occurs as a Galois group over the function field . We also develop a the…
Invariant Rational Functions, Linear Fractional Transformations and Irreducible Polynomials over Finite Fields
Rod Gow, Gary McGuire
For a subgroup of we show how some irreducible polynomials over arise from the field of invariant rational functions. The proofs rely on two actions of $P…
On a Family of Twisted Trace Curves over Finite Fields, and Fibonacci Numbers
Robin Chapman, Gary McGuire
We present some results about the number of rational points on a certain family of curves defined over a finite field. In a small number of cases the curves have more rational poin…