9 problems

Let $M$ be a finite monoid, and let $K_{\rm G}(M)$ denote its $\rm G$-kernel, the intersection of $\mu^{-1}(1)$ over all relational morphisms from $M$ to finite groups, where…

Let $\pvW$ be a pseudovariety of bands. The operator $\CFmodCTS{-}{ \mathsf{EP}_\pvW }$ is a modulus operator, and PLTC is the pointlike transfer condition relating this operator t…

Provability-completeness conjecture. An inequality $u\leqslant v$ of elements from $\Om AM$ is provable from $\Sigma$ if and only if $\op \Sigma\cl$ satisfies $u\leqslant v$.

Let $\pv U$ be the setting of the paper, let $\Sigma$ be a set of $\pv U$-pseudoidentities, and let $\op\Sigma\cl$ denote the class defined by $\Sigma$. A $\pv U$-pseudoidentity is…

Let $Q_8$ be the quaternion group of order eight and $D_4$ the dihedral group of order eight. Write $\langle\!\langle S\rangle\!\rangle$ for the compact pseudovariety generated by…

Let ${\sf Sl}$ be the pseudovariety of finite semilattices, let ${\sf L}$ be the pseudovariety of finite locally trivial semigroups, and let ${\sf GLT}$ denote the pseudovariety of…

GGM conjecture. Every pseudovariety of the form

Pin–Reutenauer conjecture. The pseudovariety $\pv G$ is strongly $\kappa$-PR.

Let $\mathcal{PODI}_n$ be the monoid of partial order-preserving or order-reversing permutations, let $\mathcal{POI}_n$ be the monoid of partial order-preserving permutations, and…