On the primeness of 2-permutability

Abstract: 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.

computational complexitycategory theorylogic

Audience: researchers in the topic

PALS Panglobal Algebra and Logic Seminar

Series comments: The PALS seminar is a research and learning seminar organized by the algebra and logic research group of the Department of Mathematics at the University of Colorado at Boulder. The scope of the seminar includes all topics with links to algebra, logic, or their applications, like general algebra, logic, model theory, category theory, set theory, set-theoretic topology, or theoretical computer science. Please contact one of the organizers for the Zoom password, to join the mailing list or if you want to speak.