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.
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