• 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



Normal Subgroup Left Identity Division Algebra Quotient Group Vector Space Versus 
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 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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