Mathematical groups.
One of the simplest and most useful algebraic structures is the group, study of which dates back to 1830. The concept is not only of mathematical interest, but has found application in fields ranging from quantum mechanics to crystallography. Despite their long history and many uses, groups remain a remote concept to many. Since the accompanying two articles concern advances in group theory and its applications, this short summary of the basic axioms and properties of groups is offered as a convenient primer.
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