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Groups

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Which of the following is an example of a group?

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A
The set of integers under addition
💡 Explanation:

A group is a non-empty set G together with an operation * (called the group operation) that combines any two elements a and b of G to form an element of G, denoted by a * b, such that the following three properties hold:

  1. Associativity: For all a, b, and c in G, (a * b) * c = a * (b * c).
  2. Identity element: There exists an element e in G such that for every a in G, e * a = a * e = a.
  3. Inverse element: For every a in G, there exists an element b in G such that a * b = b * a = e, where e is the identity element.
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