**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.