Bart de Smit, Entangled radicals

Abstract. For a field K of characteristic 0, a radical group is an abelian group B containing K^* so that each b in B has a power in K^*. If all finite subgroups of B are cyclic, then we can embed B in the multiplicative group of an extension field of K. To analyze the radical field extension K(B) of K one needs to understand relations between radicals, such as √5 + √-5 = ⁴√-100. We will show that these are controlled by the entanglement group. As an application, we formulate Artin's primitive root conjecture over number fields.