2 problems

Let $G$ be a group in the class $\mathcal{T}$ with finite $\operatorname{lcm}(G)$, and let $K\subseteq\mathbb{C}$ be any subfield closed under complex conjugation. Let…

Let $A$, $B$ and $C$ be groups, and let $G=A\ast_C B$ be their amalgamated free product. Let $K\subseteq\mathbb{C}$ be a field closed under complex conjugation, and set … Assume th…