Metabelian groups: full-rank presentations, randomness and Diophantine problems

Albert Garreta, Leire Legarreta, Alexei Miasnikov +1

We study metabelian groups $G$ given by full rank finite presentations $⟨A\mid R{⟩}_{\mathcal{M}}$ in the variety $\mathcal{M}$ of metabelian groups. We prove that $G$…