2 problems

Let $p$ be a prime and let $M$ be a locally compact group such that $Z(M)$ is open and $Z(M)\cong \mathbb{Z}_p$, $M/Z(M)$ is a Tarski monster of exponent $p$ with $p$ conjugacy cla…

A topological group is minimal if it admits no strictly coarser Hausdorff group topology. A topological group $G$ is a group retract of a topological group $M$ if there are continu…