6 problems

Weak Andrews-Curtis conjecture. Every balanced presentation of the trivial group is $Q^{**}$-equivalent to

For a Lie superalgebra with Cartan matrix generated by Chevalley generators, let non-Serre-type relations mean defining relations beyond the Serre-type relations. Non-Serre encodin…

Let $F=F_n$ be the free group of rank $n\geq 2$ with free basis $X=\{x_1,\ldots,x_n\}$. For a tuple $Y=\{y_1,\ldots,y_n\}$, write $\langle Y\rangle^F$ for its normal closure in $F$…

Let $p=2$, let $\mathcal L=\operatorname{Lie}(v_1,v_2)$ be the Fibonacci Lie algebra, and let $\mathbf L=\operatorname{Lie}_p(v_1,v_2)$ be its Fibonacci restricted version. The sou…

Let $p=2$ and let $\mathbf L=\operatorname{Lie}_p(v_1,v_2)$ be the Fibonacci restricted Lie algebra. Infinite-presentation conjecture. The algebra $\mathbf L$ is infinitely present…

Let $G$ be a group generated by a finite state automaton. Bartholdi's conjecture. The group $G$ is either finitely presented or densely related. This conjecture concerns the relati…