Laszlo Zadori (University of Szeged, Hungary), On the primeness of 2-permutability

Tue, 2 Nov 2021, 1 pm MDT

In the talk, I sketch a semantical proof of the conjecture of Garcia and Taylor that congruence permutability is a prime Maltsev condition in the lattice of interpretability types of varieties. The proof was obtained jointly with Gyenizse and Maróti, and it is based on a combinatorial property of certain digraph powers. I also discuss how the present proof is related to the proof of our earlier result on the non-primeness of n-permutability when n>4 and some other result that we obtained for 3-permutability.