Test of e-submission process [14/3/22 - 11:50]

Abstract

A group, in mathematics, is a set together with an operation that combines any two of its elements to form a third element, in such a way that the operation is associative, an identity element exists, and every element has an inverse. These three conditions, called group axioms, are familiar from number systems. The ubiquity of groups in numerous areas—both within and outside mathematics—makes them a central organizational tool in contemporary mathematics. The concept of a group arose from the study of polynomial equations, starting with Évariste Galois in the 1830s. After contributions from other fields such as number theory and geometry, the group notion was generalized and firmly established around 1870. Today, group theory is a very active mathematical discipline that studies groups in their own right. Symmetry groups are widely applied in molecular chemistry and various physical disciplines.