Isac Hedén

The derived length of subgroups of the Cremona group

We prove that the maximal derived length of a solvable subgroup of the plane Cremona group over $\mathbb C$ is equal to $5$. The main difficulty is the case of subgroups containing loxodromic elements. To treat this case, we prove that the maximal derived length of a finite solvable subgroup is $4$ and establish a cent...