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One of the major and vital concerns that occupies the central positions in Mathematic is the theory of groups.The origin of group theory can be traced to the ardent desire and attempt to determine solutions to some trending problems.Knowledge of groups now plays indispensable roles in such areas like coding theory, counting and the study of symmetries.It is notable to know that biology, chemistry and physics are mutual areas which have greatly benefited from the study and theory of groups.