GROUPS WITH BASIS PROPERTIES: A SURVEY

Abstract

This paper presents a historical study for the concepts of basis property, strong basis property, basis exchange property and exchange property by discussing the works of the previous researchers. Furthermore, some algebraic structures such as free inverse semigroup, inverse semigroup, and semigroup with some groups such as p-group, matroid group and polycyclic group have been concerned on such mentioned properties are investigated. Several examples which illustrated various notations have been presented.