Capelli-Rédei Theorem, Solvable Quintics,and Finite Fields

摘要

A situation analogous to the classic casus irreducibilis exists in the context of irreducible cubic polynomials over finite fields if it is required that solvability by radicals means solvability by irreducible radicals. In this paper we extend this analogy to irreducible quintics over finite fields by use of the Capelli-Rédei theorem.