Question

Find the order of the given element 11 in U₄₈

_{Please give me details..}

Answer 1

The element of the group U(48) are those positive numbers whose are less than 48 and prime to 48 and 1.

So the order of the group U(48) is 16.

In a group the order of the element is a least positive number such that aⁿ=e( e is the identity element of the group).

Here in U(48) the identity element is 1.

11 is an element of U(48).

Here we see that .

From this the order of the 11 in U(48) is 4.

(As the order of the group is 16 so that the order of the element only be 1, 4, 8 and 16 because the order of the element must divide order of the group)