# Group mod a subgroup

by Zorba
Tags: subgroup
 P: 77 Suppose G is a group and H is a subgroup of G. Then is G\H a subgroup itself? My feeling is it shouldn't be since 1$$\in$$H, therefore 1$$\notin$$G\H? I'm getting a bit confused about this because I'm doing a homework sheet and the question deals with a homomorphism from G $$\rightarrow$$ G\H and I'm wondering what happens to the identity element... Thanks!
 P: 948 if H is a normal subgroup, then G/H is a group. It's not a subgroup of G though since its elements are the cosets $eH=H, g_1H, g_2H, ...$, which are the images of the elements of G under that mapping. maybe I misunderstood completely though, did you get / mixed up with \ ? because G\H usually means the set {g in G | g not in H}, while G/H means quotient group