Gergő Gyenizse (University of Szeged): Digraph powers and congruence permutability

University of Szeged, Bolyai Institute, Algebra Seminar

Abstract. I sketch a semantical proof that congruence permutability is prime in the lattice of interpretability types of varieties. This proof settles a 1984 conjecture of Garcia and Taylor. The main ingredient of the proof is an entirely combinatorial statement: given two digraphs $G$ and $H$ so that each contains a universal vertex, there is a non-empty graph $ X$ so that $G^X$ and $H^X$ are isomorphic.