If G is a finite group which acts transitively on X (a set), and if H is a normal subgroup of G, show that the orbits of the induced action of H on X all have the same size.
Now I'm not sure what induce here means but i guess that it means that how H now works on X. If this is true, can I just say that H is also transitive because G is transitive and thus there is only one orbit, or am I missing something here?