Now since is a subgroup of and it means its order divides and . Therefore, . We cannot have for that would imply . A contradiction.
Therefore, the only possible case is that .
If in the group it means and therefore . But . Therefore, . Since it means the possible values for are .2. Let H be the normal subgroup G, a in G and |H|=10. The element aH of the group G/H has order 3; what are the possibilities for |a|? Explain.