Introduction to the presentation of groups

Abstract

One of the most important combinatorial group theory guarantees that given a nonempty set X, there is a group who is free on X, namely the group F := F(X) of reduced words in X. So, our fundamental purpose in this paper is to show how this group can provide a good order and subsequently use this fact to prove that every subgroup H of F has a Schreier transversal. Finally we discuss some asides about the free submission of test groups and substitution, which allows us to locate an isomorphic presentations given to the presentation of a group