The notion of group is one of the most important unifying ideas in mathematics. It draws together a wide variety of mathematical objects for which a notion of combination, or “product,” exists. Such products include the ordinary arithmetical product of numbers, but a more typical example is the product, or composition, of functions. If f, g are functions, then gf is the function whose value for argument x is f[g(x)]. (The reason for writing f[g(x)] as gf is that its meaning is “apply g, then f.” We have to pay attention to order because in general gf ≠ fg.)
KeywordsNormal Subgroup Linear Fractional Transformation Group Concept Regular Polyhedron Infinite Group
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