We establish several properties of Bulatov's higher commutator operations in congruence
permutable varieties. We use higher commutators to prove that for a finite nilpotent algebra …

For a word w in an alphabet Γ, the alternation word digraph Alt (w), a certain directed acyclic
graph associated with w, is presented as a means to analyze the free spectrum of the …

We adapt the commutator theory of universal algebra to the particular setting of racks and
quandles, exploiting a Galois connection between congruences and certain normal …

This article develops some basic properties of a congruence lattice operation, called the
higher commutator, for varieties of algebras that are congruence modular. The higher …

In [15] a generalization of Boolean circuits to arbitrary finite algebras had been introduced
and applied to sketch P versus NP-complete borderline for circuits satisfiability over …

The clone of term operations of an algebraic structure consists of all operations that can be
expressed by a term in the language of the structure. We consider bounds for the length and …

We develop the theory of the higher commutator for Taylor varieties. A new higher
commutator operation called the hypercommutator is defined using a type of invariant …

Satisfiability of Boolean circuits is among the most known and important problems in
theoretical computer science. This problem is NP-complete in general but becomes …

Let A be a finite nilpotent algebra in a congruence modular variety with finitely many
fundamental operations. If A is of prime power order, then it is known that there is a …

Given a lattice 𝕃 and a class K of algebraic structures, we say that 𝕃 forces nilpotency in K if
every algebra A∈ K whose congruence lattice Con (A) is isomorphic to 𝕃 is nilpotent. We …