Ferrari, Quartics, and Finite Fields

Summary 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 explore the situation for irreducible quartics over finite fields by use of the Capelli-Reìdei Theorem and Ferrari’s formula for the roots.