5 problems

Orbit-degree decomposition conjecture. Then $S_n$ splits as a direct sum of fields of degree $|\mathcal O_i|$ for all $i\in\{0,\dots,k\}$.

Recursive subalgebra conjecture. The set

Minority-pair conjecture. If

Given a variety $\mathcal{V}$, its residual bound $\kappa(\mathcal{V})$ is the least cardinal strictly larger than the cardinality of every subdirectly irreducible member of…

Let $\mathbf{A}$ be a finite algebra in a congruence-modular variety. An algebra is finitely related if its clone of term functions is determined by preservation of finitely many s…