Let G U16 and H 1 15 Explain why H is normal in G Identify

Let G = U(16) and H = {1, 15} Explain why H is normal in G Identify the factor group G/H

Solution

Since G = U(16), then G = {1, 3, 5, 7, 9, 11, 13, 15}, so, |G| = 8 = 2^3.

Upto isomorphism, there must be only one group of order prime power and that too, abelian.

Since \"Every subgroup of an abelian group is normal. Hence, H must be normal.

The quotient group of the factor group consists of G/H = { {1, 15}, {3, 13}, {5, 11}, {7, 9} } .