HW #1, due Nov 3

1. Let G be a group, N a subgroup. Show that the canonical projection G -> G/N can be made a group homomorphism for at most one group structure on G/N, and that there is such a group structure iff N is normal.

[Hungerford] problems:
Ch 1.2 #6,10 15bc
Ch 1.4 #6,9
Ch 1.5 #1,7,12,14