• Bernard R. Gelbaum
  • John M. H. Olmsted
Part of the Problem Books in Mathematics book series (PBM)


By definition a group is a nonempty set G and a map
$$G \times G \mathrel\backepsilon \{ x,y\} \mapsto xy \in G$$
subject to the following axioms:
  1. i

    If x, y, zG then x(yz) = (xy)z (associativity)

  2. ii
    There is in G an element denoted e with two properties:
    1. iia

      if xG then ex = x (e is a left identity);

    2. iib

      if xG there is in G a left inverse y such that yx = e





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Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Bernard R. Gelbaum
    • 1
  • John M. H. Olmsted
    • 2
  1. 1.Department of MathematicsState University of New York at BuffaloBuffaloUSA
  2. 2.Department of MathematicsSouthern Illinois UniversityCarbondaleUSA

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