3 problems

Let $G$ be an odd-order nilpotent group, with $b_{(H,\phi)}(G)$ and the local factors $\alpha_1,\alpha_2,\alpha_3$ as defined in the surrounding discussion and in Proposition. Expl…

Let $G$ be a nilpotent group, and let $c_{(H,\phi)}(G)$ be the leading constant in the constrained fair-counting asymptotic for $\operatorname{Epi}_{(H,\phi)}(G_{\mathbb{Q}},G)$. O…

Let $G$ be a non-trivial finite group and let $k$ be a number field. Write $\mathfrak{f}(K/k)$ for the product of the primes of $k$ that ramify in $K$. For…