Product Expansions Redux

TL;DR

This paper generalizes the product expansion concept for finite semigroups and offers an alternative proof for the decidability of pointlike sets within certain pseudovarieties, advancing algebraic theory.

Contribution

It introduces a new generalization of product expansions and provides a novel proof for the decidability of pointlike sets in specific pseudovarieties.

Findings

Generalized product expansion for finite semigroups

Decidability of pointlike sets proved for certain pseudovarieties

Alternative proof method enhances understanding of semigroup pseudovarieties

Abstract

We introduce a generalization of the product expansion of a finite semigroup. As an application, we provide an alternative proof of the decidability of pointlike sets for pseudovarieties consisting of semigroups whose subgroups all belong to a given decidable pseudovariety of groups.