matriarchy

/M EY1 T R IY0 AA0 R K IY0/
noun
  1. 1

    A social system in which the mother is head of household, having authority over men and children.

  2. 2

    A system of government by females (particularly as a kind of polity).

  3. 3

    The dominance of women in social or cultural systems.

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Source: https://en.wiktionary.org/wiki/matriarchy