Question

Asked Sep 4, 2019

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Show that the set {5, 15, 25, 35} is a group under multiplication modulo 40. What is the identity element of this group? Can you see any relationship between this group and *U*(8)?

Step 1

__Calculation:__

Obtain the Cayley table for the set S = {5,15,25,35} under the multiplication modulo 40 as follows.

Step 2

The above table is observed to contain all the elements of the set *S*. So, ×40 is closed and associative.

From the Cayley table the following observations are made.

- The identity element is observed to be 25, since
*x*×40 25 =*x*,*x*∈ S - The inverse of 5 is ...

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