- #1
Homo Novus
- 7
- 0
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?
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?