The smallest subgroup containing a collection of elements S is the

subgroup H with the property that if K is any subgroup containing

S then K also contains H. (So, the smallest subgroup containing S is

contained in every subgroup that contains S.) The notation for this

subgroup is <S>. In the group Z, find

a. <8, 14>

b. <8, 13>

c. <6, 15>

d. <m, n>

e. <12, 18, 45>.

In each part, find an integer k such that the subgroup is k.