if a^m was to equal the identity in G, then a^mH = H would imply that a^m is an element of H because hH = H = Hh, but i don't see how a^m could equal the identity in G
Let H be a normal subgroup of a finite group G. The order of G/H (quotient/factor group) is m. Show g^m is in H for all g in G.
Lagrange's Thm says that o(G) = o(H) * o(G/H)
xH = Hx for all x in G, since H is a normal subgroup of G
Ok, I've got a lot of statements that i believe to be...