Asked Sep 4, 2019

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)?


Expert Answer

Step 1


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


Image Transcriptionclose

15 25 35 5 40 5 25 35 5 15 25 15 15 2535 35 25 15 35 5 25 5 35 15 5

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,  ∈ S
  • The inverse of 5 is ...

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