Question

Find the order of the given element 11 in U_{48}

_{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 a^{n}=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)

(a) Give the order of each element of {1,2,3,...,10} modulo
11.
(b) Find all possible products of an element of order 2 with an
element of order 5 and show that they give primitive elements
modulo 11.

(a) Give the order of each element of {1,2,3,...,10} modulo
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(b) Find all possible products of an element of order 2 with an
element of order 5 and show that they give primitive elements
modulo 11.

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