you can prove a much stronger result: if and then this is a quick result of this well-known fact that for any group G and any subgroup H of G of finite index, there
exists a normal subgroup N of G contained in H such that
you can prove a much stronger result: if and then this is a quick result of this well-known fact that for any group G and any subgroup H of G of finite index, there
exists a normal subgroup N of G contained in H such that
Can't I deduce from the fact that since is a simple group, the only possible subgroup is {(1)} and itself, there is no subgroup of index p?