AQA
Further Paper 3 Discrete
2024
June
— Question 7
Exam Board
AQA
Module
Further Paper 3 Discrete (Further Paper 3 Discrete)
Year
2024
Session
June
Topic
Groups
7
By considering associativity, show that the set of integers does not form a group under the binary operation of subtraction.
Fully justify your answer.
7
The group G is formed by the set
$$\{ 1,7,8,11,12,18 \}$$
under the operation of multiplication modulo 19
7
Complete the Cayley table for \(G\)
\({ } ^ { \times } 19\)
1
7
8
11
12
18
1
1
7
8
11
12
18
7
7
11
8
8
7
11
11
7
12
12
11
18
18
1
7
(ii) State the inverse of 11 in \(G\)
7
State, with a reason, the possible orders of the proper subgroups of \(G\)
7
(ii) Find all the proper subgroups of \(G\)
Give your answers in the form \(\left( \langle g \rangle , \mathrm { x } _ { 19 } \right)\) where \(g \in G\)
7
(iii) The group \(H\) is such that \(G \cong H\)
State a possible name for \(H\)