4 problems

Let $\mathbb{F}^{l}$ be the free group on $l$ generators, let $\Xi$ be the normal subgroup generated by the $N$-th powers of all primitive elements, and write…

Uniform power-subgroup conjecture. There is some uniform $m\geq 2$ such that one can take

Reversible Mealy automaton conjecture. A reversible Mealy automaton cannot generate an infinite Burnside group.

Let $B$ be the group in presentation, with $n \gg 1$ chosen as in Theorem1.10, and let $f_{1,B}(x)$ denote its first Dehn function. For odd $n>10^{10}$, the verbal Dehn function of…