Edexcel FP2 AS Specimen — Question 4

Exam BoardEdexcel
ModuleFP2 AS (Further Pure 2 AS)
SessionSpecimen
TopicGroups
  1. The operation * is defined on the set \(S = \{ 0,2,3,4,5,6 \}\) by \(x ^ { * } y = x + y = x y ( \bmod 7 )\)
*023456
0
20
35
4
54
6
    1. Complete the Cayley table shown above
    2. Show that \(S\) is a group under the operation *
      (You may assume the associative law is satisfied.)
  2. Show that the element 4 has order 3
  3. Find an element which generates the group and express each of the elements in terms of this generator.
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