5 problems

Kuzmin's conjecture. The nilpotency degree satisfies

Quantitative Kurosh conjecture. Any non-linear function that occurs as the growth rate of an algebra is realizable as the growth of a nil algebra.

Let $d_{\mathbb{F}}(n,m)$ denote the maximal nilpotency index of an $m$-generated nil algebra of $n\times n$ matrices over a field $\mathbb{F}$, as defined in the paper. Derksen–Ma…

Upper-bound conjecture.

Let $G$ be a group, and let its associated Lie algebra be defined from the relevant group-theoretic filtration. Torsion-group conjecture. If $G$ is a torsion group, then its associ…