matriarchy
Definitions
noun
A social system in which the mother is head of household, having authority over men and children, and lineage is traced through the female line.
The difficulty is that when a man thinks of matriarchy, he thinks of a patriarchy with women in the place of men; he does not stop to consider that matriarchy may be a complete mirror-image. Where patriarchy establishes law, matriarchy establishes custom; where patriarchy establishes military power, matriarchy establishes religious authority; where patriarchy encourages the aresteia of the individual warrior, matriarchy encourages the tradition-bound cohesion of the collective. When, therefore, one envisions a matriarchy, one should not conjure up visions of a gang of Amazons lopping off breasts and testicles to rule by force of arms.
A system of government by females (particularly as a kind of polity).
The dominance of women in social or cultural systems.