How do subgroups of U(32) work? In particular, this problem:?

Question

Given G=U(32)
and H= U_12(32)={1;17} then G/H is abelian group of order 16/2=8
which of the three abelian groups of order 8 is it
a)Z_8
b)Z_4 +Z_2
c)Z_2+Z_2

Answer 1

hi
we use the notation U(n) in abstract algebra as aset of all positive integers less than n and relativley prime to n. (U(n) is agroup under multiplication modulo n.
ex
U(4) ={1,3}
Usub k to n i.e{U_k(n)}= {x belong to U(n) s.t xmod k=1} wher k is adivisor of n
ex
U_7(105)={1,8,22,29,43,64,71,92}