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Group Theory

  • John Stillwell
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

The notion of group is one of the most important unifying ideas in mathematics. It draws together a wide range of mathematical structures 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 and g are functions, then gf is the function whose value for argument χ 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.]

Keywords

Normal Subgroup Projective Transformation Group Concept Regular Polyhedron Infinite Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • John Stillwell
    • 1
  1. 1.Department of MathematicsUniversity of San FranciscoSan FranciscoUSA

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