Note: be sure to write in complete sentences. You will be graded on your style as well as content. I may deduct points for material you write that is correct but irrelevant, as well for material that is relevant but incorrect. A permutation of s is a bijective function from s to s: if g is a group and a is a g-set, what is the de nition of an orbit of. A maximal ideal of r is an ideal i 6= r such that there are no ideals. An element r of r is prime if r 6 r and whenever r|ab, r|a or r|b. This clearly contains the product of the groups generated by the cycles: h(1 5 3 8)ih(19)ih(4 7 6)i. This group has order 4 2 3, hence its index is the number of conjugates, hence it is the entire centralizer.
