OCR
Further Additional Pure AS
2020
November
— Question 4
Exam Board
OCR
Module
Further Additional Pure AS (Further Additional Pure AS)
Year
2020
Session
November
Topic
Groups
4
For the set \(S = \{ 2,4,6,8,10,12 \}\), under the operation \(\times _ { 14 }\) of multiplication modulo 14, complete the Cayley table given in the Printed Answer Booklet.
Show that ( \(S , \times _ { 14 }\) ) forms a group, \(G\). (You may assume that \(\times _ { 14 }\) is associative.)
Write down all the proper subgroups of \(G\).
Given that \(G\) is cyclic, write down all the possible generators of \(G\).