7 problems

Let $K$ be a quadratic number field, and write $\operatorname{Cl}(K)[2^{\infty}]$ for the $2$-primary part of its ideal class group. Gerth's conjecture. The distribution of…

A smooth 2-group is a smooth monoidal groupoid whose multiplication, associator, unitors, and inverses are smooth, and a braided smooth 2-group is a braided monoid in smooth groupo…

Let $(G_i,H_i,T_i)$, for $1\leq i\leq k$, be admissible tuples of finite $2$-groups and generating sets. Let $f_{T_i}(K)$ be the associated refined counting functions, let…

Let $G$ be a finite $2$-group and let $H\leq G$ have index $2$, with $(G,H)$ admissible. Let $f(K)$ be the associated unramified-extension counting function, let $c$ be the corresp…

Let $G$ be a finite $2$-group, let $\operatorname{rk}(G)$ denote its rank, and let $q$ be the number of rational characters of $G$. Rank-boundedness conjecture. The rank…

Let $k$ be an odd number. A finite $2$-group is 2-generated if it can be generated by two elements, and a real conjugacy class is a conjugacy class consisting of elements conjugate…

Let $r$ be an odd natural number. A finite group element is real if it is conjugate to its inverse, and a conjugacy class is real if all its elements are real. Sangroniz's conjectu…