need help for this question thank you List the elements of t

need help for this question. thank you

List the elements of the group Z_24 and determine the order of each element.

Solution

< 0 > = {0}
< 1 > = Z24
< 2 > = {0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22}
< 3 > = {0, 3, 6, 9, 12, 15, 18, 21}
< 4 > = {0, 4, 8, 12, 16, 20}
< 6 > = {0, 6, 12, 18}
< 8 > = {0, 8, 16}
< 12 > = {0, 12}

The orders of these same subgroups are:
| < 0 > | = 1 | < 1 > | = 24 | < 2 > | = 12 | < 3 > | = 8
| < 4 > | = 6 | < 6 > | = 4 | < 8 > | = 3 | < 12 > | = 2.