Sequences with idempotent products from finite regular semigroups (Q1567618)

Building on results of \textit{T. E. Hall} and \textit{M. V. Sapir} [Discrete Math. 161, No. 1-3, 151-160 (1996; Zbl 0871.20051)], which deal with the idempotent case for arbitrary finite semigroups, the author computes the smallest integer \(\alpha(n)\) such that, for every regular semigroup with \(n\) elements, every sequence of \(\alpha(n)\) elements contains a consecutive subsequence whose product is an \(\alpha\)-element, where \(\alpha\) stands for `idempotent', `core', `subgroup and core'. Dropping regularity, he obtains similar results when \(\alpha\) stands for `regular', `group', `core', `regular and core', and `subgroup and core'.