Group Theory refers to the study of algebraic structures known as groups. A group is a set of elements and an operation which can combine two elements (of the group) to form a third element. For example, consider the following equation:
s•x = t
s, x and t are all unknown variables. Group Theory is concerned with systems in which the above equation has a unique solution, which is the scenario when only one specific solution set exists. Group Theory does not concern itself with values, such as the specific value of s or t, but rather it deals with finding properties common to mathematical systems which obey a certain set of rules of Group Theory.
The basic rules of an algebraic group are as follows:
-closure: if a and b are in the group, then (s•t) is also in the group
-associativity: (s•t) •r = s•(t•r)
-identity: s•e=e•s = s
-inverses: s•s^(-1) = e
If a particular mathematical system obeys these rules, then the study of that system would form the foundation of Group Theory. Thus, understanding Group Theory is extremely important for the study of systems which are not only limited to Mathematics, but also extend into the study of Physics and Chemistry.