7 problems

Let $H,K\leqslant \operatorname{Free}[A]$ be subgroups of a free group, and write $H^w=w^{-1}Hw$. The reduced rank $\operatorname{rrk}(H)$ is the maximum of…

Let $\mathcal{F}=\prod_{\alpha\in I}^*G_\alpha$ be a free product of groups, and let $q^*$ be the minimum of the orders greater than $2$ of finite subgroups of the factors, with…

Geometric Hanna Neumann conjecture. One should have

Walter Neumann's conjecture. The set $S(H_1,H_2)$ is finite and

Imrich–Müller conjecture. The same inequality should hold whenever $H_1$ and $H_2$ satisfy conditions (C1)--(C2) specified subsequently in the source. The paper's abstract says tha…

Wise's conjecture. If $H$ or $K$ is a maximal cyclic subgroup of $F$, then

H. Neumann's intersection conjecture.