Congruence permutability is prime
Gerg\H{o} Gyenizse, Mikl\'os Mar\'oti, L\'aszl\'o Z\'adori
TL;DR
This paper proves that the property of congruence permutability is prime within the lattice of interpretability types of varieties, confirming a conjecture from 1984.
Contribution
It provides a combinatorial proof establishing the primality of congruence permutability, settling a long-standing conjecture.
Findings
Confirmed that congruence permutability is prime in the lattice of interpretability types.
Provided a combinatorial proof technique for the property.
Settled the 1984 conjecture of Garcia and Taylor.
Abstract
We give a combinatorial proof that congruence permutability is prime in the lattice of interpretability types of varieties. Thereby, we settle a 1984 conjecture of Garcia and Taylor.
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