Algebra Seminar talk
2025-04-04
Paolo Marimon
Minimal Operations over Permutation Groups
Abstract:
Joint work with Michael Pinsker. We classify the possible types of minimal operations above an arbitrary permutation group. Above the trivial group, a celebrated theorem of Rosenberg says that there are five types of minimal operations. We show that above any non-trivial permutation group there are at most four such types. Indeed, except above Boolean groups acting freely on a set, there are only three. Our results have several applications to the study of constraint satisfaction problems (CSPs). In particular, we improve an earlier classification by Bodirsky and Chen of minimal operations above oligomorphic permutation groups and answer some questions of Bodirsky related to infinite-domain CSPs.