4 problems

Bounded perfect derived subgroup conjecture. There exists an absolute constant $c$ such that $H^{(c)}$ is perfect.

Let $F$ be a free group, let $w\in F$, and let $G=F/\langle\!\langle w\rangle\!\rangle$ be the corresponding one-relator group. For a subset of $F$, write…

Malestein–Putman conjecture. The lengths of these shortest non-trivial elements have asymptotic behaviour of the form

Let the composition length of a finite group be the number of factors in a composition series, and let its derived length be the length of its derived series until the trivial grou…