Algebra Seminar talk
Equivalence of loop conditions
In a given algebra (or variety) certain identities, so called Maltsev conditions, do or do not hold. A special case of them, given only by a single identity, are called loop conditions. A loop condition implies a second one, if in every variety in which the first one holds also the second one does. An elegant way to show these implications uses the special form of these identities (which can be interpreted as a digraph) and digraph homomorphisms.
In this talk I will present some results from the paper "Loop conditions" by Miroslav Olšák in which he used the above mentioned strategy to show that there are exactly three equivalent classes of loop conditions given by undirected graphs.