Consider the group G = {1, 2, 4, 7, 8, 11, 13, 14} under multiplication modulo 15.

a) Find the multiplication table of G.

b) Is G cyclic?

c) Find 7−1

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1 Answer

s(a) In the table below, g is the element in G and p the product modulo 15.

g↓ p→

1

2

4

7

8

11

13

14

1

1

2

4

7

8

11

13

14

2

2

4

8

14

1

7

11

13

4

4

8

1

13

2

14

7

11

7

7

14

13

4

11

2

1

8

8

8

1

2

11

4

13

14

7

11

11

7

14

2

13

1

8

4

13

13

11

7

1

14

8

4

2

14

14

13

11

8

7

4

2

1

(b) The multiplication set is cyclic, because all the elements of G are revealed in each row after multiplication.

(c) What is meant by 7-1?

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