Order Let G be a group of order n Describe the possible rela

Order Let G be a group of order n. Describe the possible relation(s) between |g| and |g^2|? What condition(s) is(are) needed to imply that there exists x in G such that |x| = 2? Consider the group H5 = {1, omega, omega^2, omega^3, omega^4}, where omega^5=1. Find the order of elements, omega, omega^2, omega^3, and omega^4. Consider the group H6 = {1, omega, omega^2, omega^3, omega^4, omega^5}, where omega^6=1. Find the order of elements co, omega^2, omega^3, and omega^4. Determine the order of the elements of D_8 (the dihedral group for n=8, corresponding to symmetries of an octagon). Why are there no elements of order 3, 5, or 7? of order 6? of order 8?

Solution