Question

Let G = { 1,-1,i,-i} and N = {1,-1} be a normal subgroup of multiplicative group 'G' then find the quotient group G/N.​

Answer 1

SOLUTION

GIVEN

Let G = { 1 , -1 , i , -i } and N = { 1 , -1 } be a normal subgroup of multiplicative group G

TO DETERMINE

The quotient group G/N

EVALUATION

Here G = { 1 , -1 , i , -i } and N = { 1 , - 1 }

Here G is a commutative group and N is a normal subgroup of multiplicative group G

Now the cosets of N in G are

N = { 1 , - 1 }

iN = { i , - i }

The quotient group G/N is of order 2

The elements of G/N are N, iN

∴ G/N = { N, iN }

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