Matroids related to groups and semigroups

Abstract

Matroid is defined as a pair $(X,\mathcal{I})$, where $X$ is a nonempty finite set, and $\mathcal{I}$ is a nonempty set of subsets of  $X$ that satisfies the Hereditary Axiom and the Augmentation Axiom. The paper investigates for which semigroups (primarily finite) $S$, the pair $(\widehat{S}, \mathcal{I})$ will be a matroid.