3 problems

Solvable-radical sequence conjecture. There exists a sequence $u_n(x,y)$ such that $R(G)$ coincides with the set of elements $y\in G$ having the property that, for every $x\in G$,…

Let $\overrightarrow{u}$ be an autocorrect sequence, and let a $\overrightarrow{u}$-Engel automorphism mean an automorphism satisfying the corresponding Engel condition. Consider a…

Let $L$ be a finite-dimensional Lie algebra. For a sequence $\overrightarrow{u}=\overrightarrow{u}(x,y)$, write $L(\overrightarrow{u})$ for the corresponding ideal and let the solv…