Semigroups of centered upfamilies on groups

Аннотация

Given a group G we study right and left zeros, idempotents, the minimal ideal, left cancellable and right cancellable elements of the semigroup N_<ω(G) of centered upfamilies and characterize groups G whose extensions N_<ω(G) are commutative. We finish the paper with the complete description of the structure of the semigroups N_<ω(G) for all groups G of cardinality |G| ≤ 4.