What is authority ? Is it related to domination and the law ?
Most modern societies depend on some form of power or authority to ensure that institutions and individuals conform to establish social norms. Power (or authority) usually defined as the ability to make other do what you want regardless of what they themselves want.
(b) Dominantion : When a relationship of power or authority stable and settled, and the parties involved have become accustomed to their relative position we have a situation of domination.
If a social entity (a person, institution or group) is routinely or habitually in a position of power, it is said to be dominant.
In normal times, dominant institutions, group or individuals exercise a decisive influence or society. It is not as though they are never challenged, but this happened only in even though it implies that people are being forced to do things they don't necessarily want to do, domination in normal times can be quite ‘smooth’ in the sense of appearing to be without friction or tension.
(c) Law : In social terms, legitimacy refers to the degree of acceptance that is involved in power relations. Something that is legitimate is accepted as proper, just and fitting. In the broadest sense, it is acknowledged to be currently prevailing.
In brief, legitimacy implies conformity to existing norms of right, property and justice. Everyone must obey the lawful authority (or power) of the police office, when on duty, the policemen or policewomen has authority over the public actions of all citizens except her/his superior officers.
But police officers do not have jurisdiction over the private activities of citizens as long as they are not suspected of being unlawful in different way — different because the nature of the authority involved is less strictly or explicitly defined — the teacher has authority over her/ his pupil in the classroom. The authority of the teacher does not extend into the whole of the pupil where parents or guardians have primary responsibility and authority over their children.
A law is an explicitly codified norm or rule. It is usually written down, and these are laws that specify how laws are to be made or changed, or what is to be done if someone violates them.