OCR FP3 2013 June — Question 2

Exam BoardOCR
ModuleFP3 (Further Pure Mathematics 3)
Year2013
SessionJune
TopicGroups
  1. Write down the operation table and, assuming associativity, show that \(G\) is a group.
  2. State the order of each element.
  3. Find all the proper subgroups of \(G\). The group \(H\) consists of the set \(\{ 1,3,7,9 \}\) with the operation of multiplication modulo 10 .
  4. Explaining your reasoning, determine whether \(H\) is isomorphic to \(G\).
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