Journal of Multidisciplinary Modeling and Optimization


In this paper, we study many concepts as applications of free group, for example, presentation, rank of free group, and inverse of free group. We discussed some results about presentation concept and related it with free group. The our main result about free rank, is if G is a group, then G is free rank n if and only if G≅ Zn. Also we obtained a new fact about inverse semigroup which say there is no free inverse semigroup is finitely generated as a semigroup. Moreover, we studied some results of inverse of free semigroup, These were illustrated by formulating Theorems, Lemma, Corollaries, and all of these concepts were explained through detailed examples