2 problems

Let $G$ be a group variety defined over a number field $k$. Let $b1$ be a point of $G$, and let $B$ be the irreducible torsion variety of minimal dimension containing $b1$. The fie…

Let $p$ be a prime and let ${\mathfrak V}$ be a proper group variety. For a finite group $G$, write $\lambda_p(G)$ for its non-$p$-soluble length, and suppose that the Sylow $p$-su…