Question

Consider the multiplicative group g = {1,-1, i,- i } and h= {-l,1 } be subgroup of g, then write all possible cosets of h.

Answer 1

Answer:

h = 1 h = ( -1 ) h = { 1, -1 }  is one coset.

i h = ( -i ) h = { i, -i } is the only other coset.

These are all of the coset because we have now covered all the elements of the group g.

Alternatively, # cosets = (order of group) / (order of subgroup) = 4 / 2 = 2.

N.B. These are left cosets.  But since g is an abelian group, the right cosets are the same things.

Answer 2

Answer:

. Is the group G = {1, -1, i, i} a normal group?