Consider the group $ \mathbb z_4 \times \mathbb z_4$ of order 16 under component wise addition modulo 4. if G is union of $n$ subgroup of order 4 then minimum value of n is
a) 7
b) 4
c) 5
d) 6
My attempt:
number of elements of order 4 is 12 .these elements should be in subgroup, so minimum number of subgroup implies optimal way of putting these elements.but maximum number of element 4 in a group of order 4 is 2. hence we divide by 2 .and we get 6.
but i'm not satisfy with my answer and i feel something is wrong . is this correct ? if not, please help !