Question

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

Answer 1

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?