Group Theory
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?