If two groups are residual to a third, every group residual to one is residual to the other. The Gambier extension of this theorem states that if two groups are pseudoresidual to a third, then every group pseudoresidual to the first with an excess greater than or equal to the excess of the first minus the excess of the second is pseudoresidual to the second, with an excess .

**References**

Coolidge, J. L. *A Treatise on Algebraic Plane Curves.* New York: Dover, pp. 30-31, 1959.

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1999-05-25