Question

Let G = U(12) and N be a subgroup N = <5>. (a) Find all distinct left cosets of N in G. (b) Verify that N is normal in G. (c) What is the order of quotient group G/N? (d) Make a Cayley table for G/N.

          Let G = U(12) and N be a subgroup N = <5>.
(a) Find all distinct left cosets of N in G.
(b) Verify that N is normal in G.
(c) What is the order of quotient group G/N?
(d) Make a Cayley table for G/N.

Added by Jacob B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

03/15/2023

Step 1

Since G = U(12), it consists of all positive integers less than 12 that are relatively prime to 12. These are: G = {1, 5, 7, 11} Now, let's find the left cosets of N in G. N = (5), so we have: 1N = {1 * 5 mod 12} = {5} 5N = {5 * 5 mod 12} = {1} 7N = {7 * 5 mod Show more…

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Let G = U(12) and N be a subgroup N = <5>. (a) Find all distinct left cosets of N in G. (b) Verify that N is normal in G. (c) What is the order of quotient group G/N? (d) Make a Cayley table for G/N.