I just would like to ask for the proof of this Corollary: |a| divides |G|.
In a finite group, the order of each element of the group divides the order of the group.
(The theorem is Lagrange's Theorem: |H| divides |G|.
If G is a finite group and H is a subgroup of G, then |H| divides |G|. Moreover, the number of distinct left (right) cosets of H in G is |G|/|H|.)
p.s. (sorry!! I'm not in my mind, this must have been posted under Abstract Algebra)