The Correspondence between Composite Functions in Modern Algebra and Calculus

Abstract

The study of maps which act on a finite set of objects is of special importance in modern algebra. The main objective of this paper is to compare between the structures of groups that yield from the definition of composite functions in group theory (permutation groups) and those in calculus.

In calculus there no detailed study for groups, but we took the definition of composite functions as a binary operation to define a group. This study can be considered as an essential model for isomorphic groups.