What are the possible subgroup orders of < Z*98, x >?

Mathematics by Geoffrey

Group Theory – Mathematics

Consider the group < Z*98, x >

(a) Knowing that s((pˆ2) * q) = p* (p – 1) * (q – 1) for two distinct primes p and q. What is the order of the group?

(b) What are the possible subgroup orders of < Z*98, x >?

(c) Calculate the order of 55.

(d) Calculate the group of order 6 generated by 79 and 97. Is this subgroup cyclic?

(e) Consider H =< 19 >. What is the number of side classes of H?

(f) The quotient of < Z*98, x > by H is isomorphic to a<Zn,x> for some n?