[Modernman]

For example, in America a system of patriarchy was superimposed over an existing system of matriarchy when the Euros arrived. The matriarchy still exists although it is not recognized by the state.

One quibble here- I think you mean matrilineal rather than matriarchal. Matrilineal inheritance of property is a logical system since it is always clear who the mother of a child is, but up until recently it wasn't always, ahem, certain who the father was. Of course, a matrilineal system only works if a woman was able to independently own property, which was generally not the case in a lot of Western history.

[RightWhale]

I shall have to check with the nearest authority, who happens to be not far from here.

[RightWhale]

Okay, the local authority figure agrees that the system is matriarchal rather than matrilineal. Although she had not made the distinction before, and I hadn't either, we agree there is a distinction.