6 problems

Let $D$ be a noncommutative division algebra. A free subsemigroup is a multiplicative subsemigroup generated freely by at least two elements. Makar-Limanov's conjecture. The divisi…

Stability conjecture. For each $\delta>0$, there exists $\varepsilon>0$ such that, whenever $S\subset\mathcal{F}$ is product-free and

Extremal 3-product-free set conjecture. One of the following holds: either the letters of $\mathcal{A}$ can be labelled by $\mathbb{Z}/3\mathbb{Z}$ so that $S$ is contained in the…

Extremal $5$-, $7$-, and $13$-product-free set conjecture. For $k=5,7,13$, the extremal sets are exactly the sets described by the paper's structural theorem for $k$-product-free s…

Leader–Letzter–Narayanan–Walters conjecture. If $S\subset\mathcal{F}$ is product-free and $d^{\ast}(S)=1/2$, then

Uniqueness conjecture. If $S\subset\mathcal{F}_{\mathscr{A}}$ is product-free and