Sequences with idempotent products from finite regular semigroups Original Research Article

We find the smallest integer α(n) such that for every regular semigroup S of order n, every sequence of length α(n) of elements of S contains a consecutive subsequence whose product is an α-element, where α= ‘idempotent’, ‘core’ and ‘subgroup and core’. For arbitrary semigroups of order n, we also find α(n) where α= ‘regular’, ‘group’, ‘core’, ‘regular and core’ and ‘subgroup and core’.