Non self-similar metabelian groups

Abstract

We show some sufficient conditions for a finitely presented group $G=A⋊Q$, with $A$ and $Q$ abelian and the Krull dimension of $A$ equals to $2$ to be not self-similar. This is in contrast to the case of the Krull dimension of $A$ equals to $1$ considered by Kochloukova and Sidki in 2020.

25 pages