Radical extensions and crossed homomorphisms

Abstract

If Ω/F is a Galois extension with Galois G and μ(Ω) denotes the group of roots of unity in Ω, we use the group Z1 (G,μ(Ω)) of crossed homomorphisms to study radical extensions inside Ω. Furthermore, we characterise cubic radical extension, and we provide an example to show that this result can not extended for higher degree extensions.