Hegemony
In the 19th century, hegemony came to denote the "Social or cultural predominance or ascendancy; predominance by one group within a society or milieu". Later, it could be used to mean "a group or regime which exerts undue influence within a society". Also, it could be used for the geopolitical and the cultural predominance of one country over others, from which was derived "hegemonism", as in the idea that the Great Powers meant to establish European hegemony over Asia and Africa.
Alexander J. Motyl
Motyl also posits varying degrees of empire: "formal", "informal", and "hegemonic". In a formal imperial relationship, the core can appoint and dismiss peripheral elites, obviate any external agenda or policies, and directly control the internal agenda and policies. In an informal imperial relationship, the core has influence but not control over appointing and dismissing peripheral elites, direct control over the external agenda and policies, and influence over the internal agenda and policies. Finally, in a hegemonic relationship, the core has no control over appointing or dismissing peripheral elites, control over the external agenda, influence over external policies, and no control over the internal agenda or policies.