Is "order" = "size"? I'm really confused... we refer to the "size" of a group as the "order"... But are they really equivalent? Can we prove that simply? Example: Say we have a group G and a subgroup H. Then take one of the cosets of H, say Hx... It has order = o(G)/o(G/H). But does this mean that in G/H, (Hx)^[o(G)/o(G/H)] = e = H?? Or do elements have different orders in different groups? I'm so confused. Oh, and this whole factor group thing... Does this only apply to normal subgroups?